## Limits of n-th roots

### Task number: 2871

Determine the following limits.

#### Variant 1

\(\displaystyle \lim_{n\to\infty}\root{n}\of{n} \)

#### Variant 2

\(\displaystyle \lim_{n\to\infty}\root{n}\of{n^2+2^n+3^n}. \)

#### Variant 3

\(\displaystyle \lim_{n\to\infty}\sqrt[n]{a^n+b^n+c^n} \), where \(a,b,c>0\) are given real numbers.

#### Variant 4

\(\displaystyle \lim_{n\to\infty}\sqrt[n]{n!} \)