someone please help me with this. show that the convergence of a series is not affected by changing a finite number of its terms.

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- Sep 21st 2009, 05:25 PM #1

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- Sep 21st 2009, 08:20 PM #2
Since there are only finitely many terms being changed, let $\displaystyle N=\max\{i:a_i~changed\}$

Rewrite the sum as $\displaystyle \sum_{i=1}^N a_i+\sum_{i=N+1}^{\infty}a_i$.

The left sum is just adding a finite list of numbers, so it is just a number, and the convergence of the right sum is implied by the convergence of the original sum $\displaystyle \sum_i a_i$. Thus the whole sum converges.

- Sep 22nd 2009, 04:20 PM #3

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