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Essential Calculus: Early Transcendentals
Found in: Page 425
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Short Answer

Explain what it means to say that\(\sum\limits_{n = 1}^\infty {{a_n}} = 5\).

It means that series converges to\(5\).

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Step by Step Solution


A convergent series is an infinite sum of a sequence of numbers\(\sum\limits_{n = 1}^\infty {{a_n}} \) that adds up to finite number.


Given a series \(\sum\limits_{n = 1}^\infty {{a_n}} = 5\)

It means that the sum of the infinite terms of the sequence \(\left\{ {{a_n}} \right\}\)is equal to 5.

i.e \({a_1} + {a_2} + {a_3} + \cdots \cdots = 5\)

We know that\(\mathop {\lim }\limits_{k \to \infty } {S_k} = \sum\limits_{n = 1}^\infty {{a_n}} \)where\({s_k}\)denotes the \({k^{{\rm{th }}}}\)partial sum of series.

Then, \(\mathop {\lim }\limits_{k \to \infty } {s_k} = 5\)and says that the series\(\sum\limits_{n = 1}^\infty {{a_n}} \)converges to 5.

And 5 is called the sum of the series\(\sum\limits_{n = 1}^\infty {{a_n}} \).

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