Question

Determine whether the series converges or diverges

Answer 1

\[\sum_{n=1}^{\infty}\frac{ 5 }{2n ^{2} +4n+3}\]

Answer 2

the degree of the numerator is 0
the degree of the denominator is 2
\(2-0=2\) and since \(2>1\) this converges by the famous "eyeball test"

Answer 3

what if i need to show my work like for an exam?

Answer 4

hmmm

Answer 5

use the comparison test
compare it to
\[\sum_{n=1}^{\infty}\frac{1}{n^2}\] a "p" series where \(p=2\) and since \(2>1\) \[\sum\frac{1}{n^2}\] converges and therefore your series does as well

Answer 6

why did you choose to compare it to 1/n^2?

Answer 7

because the degree of the denominator is 2 and the degree of the numerator is 0
what else could i compare it to?

Answer 8

oh ok so when i have a problem like that I just check for the degrees and that's how i can get an equation to compare it to?