## Series

### Task number: 2901

Compute the sums of the following sequences.

#### Variant 1

\(\displaystyle \sum_{n=0}^{\infty}\frac{3^n-2^{n+1}}{6^n} \).

#### Variant 2

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

#### Variant 3

\(\displaystyle \sum_{n=1}^{\infty}\frac1{4n^2-1} \).

#### Variant 4

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

#### Variant 5

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

#### Variant 6

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