## Comparison test

### Task number: 2930

Investigate the convergence of the sequences.

#### Variant 1

\(\displaystyle \sum_{n=1}^{\infty}\frac{1}{2n+1} \)

#### Variant 2

\(\displaystyle \sum_{n=1}^{\infty}\frac{1}{(2n+1)^2} \)

#### Variant 3

\(\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^2-4n+5} \).

#### Variant 4

\(\displaystyle \sum_{n=1}^{\infty}\frac{2n^2+3n+4}{2n^2+5} \)

#### Variant 5

\(\displaystyle \sum_{n=1}^{\infty}\frac{2n^2+3n+4}{(2n^2+5)^2} \)

#### Variant 6

\(\displaystyle \sum\limits_{n=1}^{\infty} \frac{2n^2 + 1}{n^3} \).

#### Variant 7

\(\displaystyle \sum\limits_{n=1}^{\infty} \frac{n^3 - 1}{n^4 + n^2}. \)

#### Variant 8

\(\displaystyle \sum\limits_{n=1}^{\infty} \frac{6^n + 7^n}{8^n - 2^n}. \)

#### Variant 9

\(\displaystyle \sum_{n=1}^{\infty}\frac{1}{(n+1)\sqrt{n+2}} \)

#### Variant 10

\(\displaystyle \sum_{n=1}^{\infty}\frac{1}{\sqrt{2n+1}\sqrt{2n+3}} \)

#### Variant 11

\(\displaystyle \sum\limits_{n=2}^{\infty} \frac{1}{\root 5 \of{n^4 + n} \root 3 \of{n-2}}. \)