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

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

Difficulty level: Easy task (using definitions and simple reasoning)
Proving or derivation task
Cs translation
Send comment on task by email