## Squeezed sequences

### Task number: 2867

Using the squeeze lemma, determine the following limits.

#### Variant 1

\(\displaystyle \lim_{n\to\infty} \frac{(-1)^n}n\)

#### Variant 2

\(\displaystyle \lim_{n\to\infty} \frac1n \sin n^2 \)

#### Variant 3

\(\displaystyle \lim_{n\to\infty}\frac{n}{2^n} \)

#### Variant 4

\(\displaystyle \lim_{n\to\infty}\frac{n^k}{n!} \), pro \(k\in \mathbb N\)

#### Variant 5

\(\displaystyle \lim_{n\to\infty}\frac{2^n}{n!}. \)

#### Variant 6

\(\displaystyle \lim_{n\to\infty}\frac{q^n}{n!} \), pro \(q\in \mathbb R\).

#### Variant 7

\(\displaystyle \lim_{n\to\infty}\frac{n!}{n^n} \)