1. ## hw problem

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

2. Originally Posted by gixxer998
someone please help me with this. show that the convergence of a series is not affected by changing a finite number of its terms.
Since there are only finitely many terms being changed, let $N=\max\{i:a_i~changed\}$

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

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 $\sum_i a_i$. Thus the whole sum converges.

3. Thank you so much for your help!