## Comparison test

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

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