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Partial sums: formula for nth term from partial sum (video) | Khan A…
The sum of the terms of a sequence is called a series. To find the sum of a certain number of terms of an arithmetic sequence: The sum of an arithmetic series is found by multiplying the number of terms times the average of the first and last terms. where Sn is the sum of n terms (nth partial sum), a1 is the first term, an is the nth term.
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[DOC File]Department of Mathematics : The University of Akron
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If a sequence has a finite limit as , we say that the sequence converges to that limit. If a sequence does not have a finite limit as , then we say that the sequence diverges. ... If the series has a sum S, then , where is the nth partial sum of the series. In other words, if the three conditions are met, you can approximate the sum of the ...
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[DOC File]Sequences
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Extension. Consider the series 8 + 4 + 2 + 1 + … developed in Part 1 of this activity. Recall that the sum was determined to be 16. Now consider the sequence of partial sums for this series: 8, 12, 14, 15, 15.5, 15.75, … Write a rule for the sequence of partial sums. Graph the series on your graphing calculator on the window [0,20] X [0,17].
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[DOC File]Section 1 - Radford
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Remember a series is the sum of the terms of a sequence. A partial sum, Sn, of an infinite series is the sum of its first n terms. Now, let’s treat the sequence developed in #1 – 7 as a series. 8. Find the following partial sums of our sequence. n Write the Partial Series Here Sn 1 8 8 2 8 + 4 12 3 8 + 4 + 2 14 4 8 + 4 + 2 + 1 15 5
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[DOC File]Arithmetic Sequences
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Sequence an infinite set of ordered numbers. 1, 4, 9, 16, 25,… is the sequence of perfect squares. Series the sum of all the terms of a sequence. 1 + 4 + 9 + 16 + 25 + … is the series of perfect squares. Partial sum the sum of the first n terms of a sequence. is the third partial sum of the series of perfect squares.
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[DOC File]CHAPTER 7: SEQUENCES, SERIES, AND COMBINATORICS
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Given an infinite sequence , then . is called an infinite series. Note: is the infinite sequence . is an infinite series. Consider. Note that is a sequence of numbers called a sequence of partial sums. Definition: For an infinite series , the partial sum is given by. If the sequence of partial sums converges to S, the series converges.
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[DOC File]Sequences and Series**
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partial sum. is the sum of the first n terms A partial sum is also called a . finite series. or . nth partial sum, and is denoted . Sigma Notation: The Greek letter (sigma) can be used to denote a sum when the general term of a sequence is a formula. Example: The sum of the first four terms of the sequence 3, 5, 7, 9, . . ., , . . . can be named
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Partial sum of a sequence