## anonymous 4 years ago Determine whether the series converges or diverges. (Answer: converges) sum from n=1 to infinity of (n^2 + 2^n)/(n + 3^n)

1. anonymous

$\sum_{n=1}^{\infty}(n^2 + 2^n)/(n + 3^n)$

2. mathmate

Divide top and bottom by n^2 (1+2^n/n^2)/(1/n+3^n/n^2) as n->inf, 1 and 1/n drop off: (2/3)^n Use ratio test as n-> inf a(n+1)/a(n) =(2/3)=2/3 < 1 so the series converges.