I was asked to evaluate the summation of [tex]\frac{1}{n(n+1)}[/tex] from n=1 to infinity(adsbygoogle = window.adsbygoogle || []).push({});

I used partial fractions to obtain [tex]\frac{1}{n}[/tex] - [tex]\frac{1}{n+1}[/tex]

From here I don't understand how to evaluate. In my solutions manual, they plugged in values from 1 to infinity showing (1 - 1/2+ (1/2 - 1/3)...etc and created a new series called S_{n}= 1 - [tex]\frac{1}{n+1}[/tex] then took the limit of that to infinity to get the answer 1.

How would I know what S_{n}should be?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: How to evaluate what a series converges to?

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