I have tried solving this question. It would be great if someone gives some idea about how to go about solving this question.
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2.401615526026297355671587971656109034016639552161016527027633818278874921157513254553304977301472975629176075585565071836891089801877839776658934761375622082021212395176704512873346502372092553984611... – Hagen von Eitzen Apr 04 '15 at 17:46
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Define: $$a_n=\sqrt{4+\sqrt[3]{4+\sqrt[4]{4+\sqrt[5]{4+ .......\sqrt[n]{4} }}}}$$ and determine the limit of this sequence!! – Elaqqad Apr 04 '15 at 17:50
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Two long comment, this question is related to other question, but it seems that there is no closed form from thier realively partiel answers:
- Evaluating the sum $\lim_{n\to \infty}\sqrt[2]{2+\sqrt[3]{2+\sqrt[4]{2+\cdots+\sqrt[n]{2}}}}$
- Problem 6 - IMO 1985
- How to find this limit: $A=\lim_{n\to \infty}\sqrt{1+\sqrt{\frac{1}{2}+\sqrt{\frac{1}{3}+\cdots+\sqrt{\frac{1}{n}}}}}$
- Find the limit $L=\lim_{n\to \infty} \sqrt{\frac{1}{2}+\sqrt[3]{\frac{1}{3}+\cdots+\sqrt[n]{\frac{1}{n}}}}$
Elaqqad
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