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Calculus Level 2

Find the limit $\lim_{x\to 0}\left(\sum_{k=1}^n\sqrt[x]{k}\right)^x$ If you think limit doesn't exist. Enter your answer as 1111.

Source: Maths fact , posted by Pierre Mounir . One may wish to do Euler appear at a time .

1 solution

Théo Leblanc
Apr 15, 2020

Hint : the limit does not exists because limits when $x\to 0^+$ and $x\to 0^-$ both exists but are different when $n>1$ .

Exactly, those two different limits are $1/2$ and $n$ .

Naren Bhandari - 1 year, 1 month ago