Find the limit $\lim_{n\to\infty}\sqrt{1+\sqrt{2+\cdots+\sqrt{n}}}$

Asked May 15 '13 at 02:21

Active May 15 '13 at 02:21

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Find the limit $$\lim_{n\to\infty}\sqrt{1+\sqrt{2+\cdots+\sqrt{n}}}$$. Remark:there are n times square root within $n$.

asked May 15 '13 at 02:21

XLDD

1

Following the link above, it looks like (albeit the sequence is convergent) no closed-form expression is known for its limit: http://oeis.org/A072449/internal – Clement C. May 15 '13 at 02:37

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