Interesting Limit (17)

Calculus Level 4

Let F n F_n be the n th n^\text{th} Fermat number 2 2 n + 1. \large 2^{2^{^n}}+1. Find

lim ⁡ n → ∞ 6 F 1 + 6 F 2 + 6 F 3 + ⋯ + 6 F n . \lim_{n\to\infty}\sqrt{6F_1+\sqrt{6F_2+\sqrt{6F_3+\sqrt{\dots+\sqrt{6F_n}}}}}.


The answer is 6.5.

Brian Lie by Brian Lie , 26, China

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1 solution

This is The Problem 11967 in American Mathematical Monthly, Vol.124 ,March 2017

I found this on the Internet. My answer was a guess.

Click here to get the pdf of this solution on right.

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