(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\sum_{n=1}^{\infty}\frac{8\arctan{n}}{1+n^2}[/tex]

2. Relevant equations

3. The attempt at a solution

so im comparing it to the integral [itex]\int_{1}^{\infty}\frac{8\arctan{x}}{1+x^2}[/itex]

but at first i need to show that the function im integrating is continuous, positive and decreasing. I know its continuous and positive from 1 to infinity but i need to show that it is decreasing

so i found the derivative of the function and got [itex]\frac{8-16x\arctan{x}}{(1+x^2)^2}[/itex] but i got stuck trying to find the critical points

specifically i forgot how to solve equations like [itex]8-16x\arctan{x}=0[/itex], mainly just because of that extra x in front of the arctan

i know this boils down to more of a precalc problem but i posted this on the calc homework help because i thought maybe some of my earlier steps were wrong

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Using the integral test to test for divergence/convergence

**Physics Forums | Science Articles, Homework Help, Discussion**