Given the Infinite Series 1/(1+n^2) where n goes from 1 to infinity, show that the sum is less than pi/2.
Series goes 1/2, 1/5, 1/10, 1/17, 1/26 and so on
The Attempt at a Solution
I have tried to find a telescoping series, but I can't see to get the terms to cancel out. My next try was to find the partial sum of the series, but I seem to want to take the integral from 1 til n+1 (as a form of partial sum) of 1/(1+n^2). I end up with Arctan(1+n) - Arctan(1), which obviously is less than pi/2, but I don't find this as a credibal solution....
Could anyone try to give me any hints on which way to go, or what way to go?
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