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## Homework Statement

Use the integral test to show that the sum of the series

gif.latex

##\sum_{n=1}^\infty \dfrac{1}{1+n^2}##

is smaller than pi/2.

## Homework Equations

## The Attempt at a Solution

I know that the series converges, and the integral converges to pi/4. As far as I´ve understood, this does however not mean that the series converges to pi/4. How should I solve this?

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