Answer
Convergent
Work Step by Step
Step 1: Restate The Problem
Step 2: Create a function f(n) using the series
Step 3: Use Divergence Test
Problem:
$\sum^\infty_{n=1} \frac{1}{n^2+2n+2}$
Test for Divergence Using Divergence Test:
$f(n) = \frac{1}{n^2+2n+2}$
Series is convergent if $ \lim\limits_{n \to \infty} f(n) =0$
$\lim\limits_{n \to \infty} \frac{1}{n^2+2n+2} = \frac{1}{\infty} = 0$
Thus, Series is convergent by Divergence Test
