Fresh features from the #1 AI-enhanced learning platform.Try it free
Fresh features from the #1 AI-enhanced learning platformCrush your year with the magic of personalized studying.Try it free
Question

# Test for convergence.$\sum_{n=1}^{\infty} \frac{\sqrt{n}+n+n^{3 / 2}}{\sqrt{n}+n+n^{5 / 2}+n^3}$

Solution

Verified
Step 1
1 of 4
Let $\sum a_n$ be the given series and $\sum b_n$ be the series we compare. The ratio comparison test states that $1)$ If $\sum b_n$ is a convergent series with $\lim_{n \to \infty}(|a_n|/b_n)<\infty$, then $\sum a_n$ converges. $2)$ If $\sum b_n$ is a divergent series with $\lim_{n \to \infty}(|a_n|/b_n)>0$, then $\sum a_n$ diverges.

## Recommended textbook solutions #### Thomas' Calculus

14th EditionISBN: 9780134438986 (8 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,144 solutions #### Calculus II

2nd EditionISBN: 9780387909752Alan Weinstein, Jerrold E. Marsden
1,698 solutions #### Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (5 more)James Stewart
11,085 solutions #### Calculus: Early Transcendentals

9th EditionISBN: 9781337613927Daniel K. Clegg, James Stewart, Saleem Watson
11,048 solutions