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Topic: Partial sum

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Arithmetic progression

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	partial_sum (Standard C++ Library Reference)
		Computes a series of sums in an input range from the first element through the ith element and stores the result of each such sum in the ith element of a destination range or computes the result of a generalized procedure where the sum operation is replaced by another specified binary operation.
		An input iterator addressing the last element in the range to be partially summed or combined according to a specified binary operation that is one position beyond the final element actually included in the iterated accumulation.
		The binary operation that is to be applied in the generalized operation replacing the operation of sum in the partial sum procedure.
	msdn.microsoft.com /library/en-us/vcstdlib/html/vclrf_numeric_Partialsum.asp?frame=true (397 words)

	Formal-Numeric Series (Site not responding. Last check: 2007-10-20)
		Specifying the partial sums implies an ordering that removes infinitely many degrees of freedom from the evaluation of a series.
		In general, since the nth partial sum of the natural sequence is n(n+1)/2, and the mth partial sum of the geometric sequence 1 + b + b^2 +...
		is (b^m - 1)/(b-1), we have a case of equal partial sums for every pair of integers n,m such that n(n+1)/2 = (b^m - 1)/(b-1).
	www.mathpages.com /home/kmath500.htm (448 words)

	Partial Lump Sum - Frequently Asked Questions
		Partial Lump Sum allows you to receive a portion of your retirement benefit as a one-time payment in exchange for a permanently reduced monthly retirement allowance.
		It is a good idea to use the Retirement Benefits Calculator for a personalized estimate of the Partial Lump Sum and its impact on your monthly allowance because the amount is specific for each member's account.
		If the Partial Lump Sum is not rolled over into an eligible plan, CalSTRS must withhold 20 percent for federal income tax and 6 percent California State income tax unless you specify that no State income tax is to be withheld on the taxable portion of the distribution.
	www.calstrs.com /Help/faqs/plsfaqs.aspx (1433 words)

	Device for multiplying binary numbers - Patent 4293922
		Each partial sum forming device furthermore comprises j outputs for outputting a partial sum of the signals received by the partial sum forming device and a carry output for outputting, simultaneously therewith, a binary output carry signal to a partial sum forming device of next-higher significance level, if applicable.
		The outputs of the partial sum forming units 134, 135 are connected in parallel to the inputs of the unit 136.
		The outputs of the pairs of partial sum forming units 137/138 and 139/141 are connected in parallel to the inputs of the partial sum forming units 139 and 142, respectively.
	www.freepatentsonline.com /4293922.html (6620 words)

	PlanetMath: sum of series
		of real or complex numbers is convergent and the limit of its partial sums is
		The sum of the series is equal to the sum of a partial sum and the corresponding remainder term.
		This is version 8 of sum of series, born on 2004-11-18, modified 2006-09-24.
	planetmath.org /encyclopedia/PartialSum.html (99 words)

	PlanetMath: a lecture on the partial fraction decomposition method
		to a sum of integrals of the types described in the previous sections.
		as the sum of partial fractions of the types discussed in the previous section.
		This is version 1 of a lecture on the partial fraction decomposition method, born on 2006-02-02.
	planetmath.org /encyclopedia/ALectureOnThePartialFractionDecompositionMethod.html (548 words)

	Apparatus for decimal multiplication - Patent 4677583
		At a final cycle, the sum and carry from the carry save adder are added by a full adder, and the subtraction of 6 is made for each digit according to the existence of carry transfer in each digit of the full adder and the resultant value is output as a multiplication result.
		For example, where the sum output S and the carry output C of the carry save adder for a certain decimal digit are S="6" and C="3", respectively, C' is C'="6" or C'="7" depending upon whether the value of C of the lower order digit of the pertinent decimal digit is "0"-"7" or "8"-"F".
		The sum output S subjected to the first correction is selected as S' and the value resulting from the one bit left shift of the carry output of the carry save adder is employed as C'.
	www.freepatentsonline.com /4677583.html (6939 words)

	Hardware Binary Arithmetic
		Then the tens column is added next, etc. If the sum is greater than or equal to ten, the least significant digit is written as a partial sum and a carry of 1 is added to the sum of the next column.
		The partial sum is 0 which is the least significant bit of the result and the carry of 1 is added to the bits in the second column from the right.
		Thus the partial sum of 1 is written in the second column from the right.
	cs.uhh.hawaii.edu /cs/courses/cs100/Hardware/hardbina.htm (973 words)

	New York State Comptroller - New York State and Local Retirement System -Partial Lump Sum Payments, FAQ
		Lump sum payments are a percentage of the actuarial value of your retirement benefit at the time you retire.
		However, you must repay the partial lump sum distribution that was made to you.
		You can read our brochure, Partial Lump Sum Payment at Retirement, available on our website, contact our Call Center toll-free at 1-866-805-0990 or 518-474-7736 in the Albany, New York area or meet with an Information Representative at any of our 16 consultation sites.
	www.osc.state.ny.us /retire/publications/partial_lump_sum_payment_option/frequently_asked_questions.htm (697 words)

	Partial Sums
		Having the information we found in problem (1a) regarding the convergence or divergence of each series, we will now look at some of the partial sums of these series to illustrate how important the integral test is in providing us with immediate insight into the convergence and divergence of a series.
		Note that the x-coordinate indicates which partial sum we are considering and the y-coordinate is that partial sum.
		To start with a partial sum other than the first, or to end with a partial sum different from the tenth, just adjust the arguments in the command.
	www.math.wpi.edu /Course_Materials/MA1023C99/partsums/node1.html (1173 words)

	supplemental20
		Well, we could start creating sums of a finite number of terms, called partial sums, and determine if the sequence of partial sums converge to a number.
		If the sequence of partial sums converge to a limit L, then we can say that the series converges and its sum is L. If the sequence of partial sums of the series does not converge, then the series diverges.
		Therefore it converges and its sum is 3.
	faculty.eicc.edu /bwood/ma155supplemental/supplemental20.htm (775 words)

	Series (mathematics) Summary
		Thus, in general, the sum of an infinite series is the limit of the sequence of partial sums as n grows without bound, provided that such a limit exists.
		If the sequence of partial sums continues to grow without bound as n grows without bound, then the infinite series does not have a sum and is said to diverge.
		Because F is not totally ordered, and because there may be uncountably many finite partial sums, this is not a limit of a sequence of partial sums, but rather of a net.
	www.bookrags.com /Series_(mathematics) (3434 words)

	Infinite Series
		A series will not converge if the sequence being summed does not converge to zero, but just because a sequence converges to zero does not mean that the sum of the sequence will converge.
		In this case, you could look at the sequence and see that for all but the first few terms, the sum of any two sequential terms is larger than the term preceding it in the sequence.
		Following this logic, for any term in the sequence there is a sum of higher index terms that are greater than that term in the sequence, and the sequence will not converge.
	charon.kean.edu /~djoiner/book_1603/node91.html (336 words)

	Arithmetic Series
		An arithmetic series is the sum of an arithmetic sequence.
		The "partial" sum is the sum of a limited (that is to say, finite) number of terms, like the first ten terms, or the fifth through the hundredth terms.
		th partial sum is the sum of the first thirty-five terms.
	www.purplemath.com /modules/series4.htm (324 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-20)
		A sequence of elements (called the terms of the given series) of some linear topological space and a certain infinite set of their partial sums (called the partial sums of the series) for which the notion of a limit is defined.
		If the sequence of partial sums of the series (2) does not have a finite limit, then the series is called divergent (cf.
		A condition for the convergence of a series which does not use the notion of its sum is the Cauchy criterion for the convergence of a series.
	eom.springer.de /s/s084670.htm (2297 words)

	Search ScienceWorld
		Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation.
		A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation (partial^2psi)/(partialx^2)+(partial^2psi)/(partialy^2)+(partial^2psi)/(partialz^2)==1/(v^2)(partial^2psi)/(partialt^2).
		Partial evaluation is a branch of computer science studying program transformation via specialization.
	scienceworld.wolfram.com /search/index.cgi?num=&q=Partial (410 words)

	7.2 - Arithmetic Sequences (Site not responding. Last check: 2007-10-20)
		partial sum or the sum of the first n terms of the sequence.
		Therefore, the sum of the first n terms of an arithmetic sequence is S
		When the lower limit of the summation is 1, there is little problem figuring out what the number of terms is. However, when the lower limit is any other number, it seems to give people difficulty.
	www.richland.edu /james/lecture/m116/sequences/arithmetic.html (613 words)

	Jeanne Ward
		A review of the voluminous filings in this case shows that the amount of the benefits due her are not in dispute, rather the respondent (insurer) resists any partial lump summing and requests that the matter be dismissed on account of claimant's failure to provide it with a detailed justification for her lump-sum request.
		The insurer argues that even though the parties mediated the claimant's lump-sum request the petitioner nonetheless failed to comply with mediation requirements since she has never provided respondent with a detailed justification for her lump-sum request.
		In inserting specific justification requirements with respect to lump summing of permanent total disability benefits, and omitting any similar requirements with respect to lump summing of permanent partial disability benefits, the legislature has indicated that no justification is required.
	wcc.dli.mt.gov /W/WARD_J_SR.htm (1268 words)

	OPERS - Helping You Achieve a Secure Future (Site not responding. Last check: 2007-10-20)
		The Partial Lump Sum Option Payment (PLOP) is a method in which a member, at the time of retirement, may elect to receive a partial lump sum payment amount and a reduced monthly allowance.
		The lump sum payment cannot be less than six times or more than thirty-six times the monthly amount that would be payable to the member under the plan of payment selected and shall not result in a monthly allowance that is less than fifty percent of that monthly amount.
		The total amount paid as a lump sum and a monthly benefit shall be the actuarial equivalent of the amount that would have been paid had the lump sum not been selected.
	www.opers.org /member/news/plop.shtml (504 words)

	18.013A Calculus with Applications, Fall 2001, Online Textbook
		Obviously it is not enough to compute the partial sums of the series up to the fifth or twenty fifth term and estimate the series sum as the fifth or twenty fifth partial sum.
		The sequence sum is therefore trapped between any pair of successive values of the partial sums.
		In other words, the error in estimating this sum as noted from its first 5 terms is on the order of one hundredth of a percent.
	ocw.mit.edu /ans7870/18/18.013a/textbook/chapter_a/contents.html (612 words)

	Absolute and Conditional Convergence
		If the partial sums of the positive terms of s are bounded, and the partial sums of the negative terms of s are bounded, then s would be absolutely convergent.
		Given ε, find an n such that the partial sums of the original series (beyond n) are within ε/2 of s, and at the same time, the terms of the series (which go to zero) are bounded by ε/2.
		The remaining partial sum is within ε/2 of s, and the last term, which we can bring back in, is bounded by ε/2.
	www.mathreference.com /lc-ser,abs.html (807 words)

	The Integral and Comparison Tests
		From the graph of the first 20 partial sums shown in Figure 8.26, it appears that the series converges to some value near 0.3.
		From the graph of the first 20 partial sums seen in Figure 8.27, it appears that the partial sums are growing very rapidly.
		The graph of the first 20 partial sums seen in Figure 8.28 looks somewhat similar to the graph in Figure 8.26, except that the series appears to be converging to about 0.12.
	euphrates.wpunj.edu /courses/maen507/Week14/section03.htm (1563 words)

	ReuvenLax : Divergent Series
		A convergence definition was probably given as the convergence of the sequence of partial sums of the series.
		The sequence of partial sums of the harmonic series closely approximate the natural logarithm function.
		The partial sums of this series are 1, 0, 1, 0,...
	blogs.msdn.com /reuvenlax/archive/2006/01/09/510732.aspx (1159 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		These partial sums are then added to a global sum.
		The global sum is a shared variable and hence the access to it is controlled by using locks.
		Sum of numbers from 1 to 200 is 20100
	mason.gmu.edu /~vdevadas/threadC.html (334 words)

	Chinese Mathematics: Rebecca and Tommy (Site not responding. Last check: 2007-10-20)
		The first coefficient is multiplied by the approximate root and added to the second coefficient, making the first partial sum of the first set.
		The first coefficient is multiplied by the approximate root and added to the first partial sum, making the second partial sum of the first set.
		The first partial sum is multiplied by the approximate root and the product is added to the third coefficient, making the first partial sum of the second set.
	www.roma.unisa.edu.au /07305/chin.htm (302 words)

	Annuity Options (Site not responding. Last check: 2007-10-20)
		At retirement, you may select the standard annuity, a partial lump sum option, or one of five survivor options.
		Your choice of the standard annuity, partial lump sum, or one of the options cannot be changed.
		Your annuity amount after the lump sum distribution would be reduced further to 92.7% of the reduced amount, or $836.15.
	www.ers.state.tx.us /retirement/AnnuityOptions.htm (1244 words)

	partial_sum
		Computes a series of sums in an input range from the first element through the ith element and stores the result of each such sum in the ith element of a destination range or computes the result of a generalized procedure where the sum operation is replaced by another specified binary operation.
		An input iterator addressing the last element in the range to be partially summed or combined according to a specified binary operation that is one position beyond the final element actually included in the iterated accumulation.
		The binary operation that is to be applied in the generalized operation replacing the operation of sum in the partial sum procedure.
	windowssdk.msdn.microsoft.com /en-us/library/et8wc8tt(VS.80).aspx (413 words)

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