Another Unexpected Number?

Calculus Level 3

x = 1 + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + … \large x=1+\frac{1}{1+\frac{2}{1+\frac{3}{1+\frac{4}{1+\frac{5}{1+\dots}}}}}

Find x x to 3 decimal places. ( Inspiration )

Bonus : Can x x be written in terms of a constant? If so, how?


The answer is 1.525.

Blan Morrison by Blan Morrison , 18, USA

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1 solution

Aaghaz Mahajan
Nov 18, 2018

@Blan Morrison This one is a known continued fraction which has its closed form in terms of complementary error function...........!! Check out this link.....
http://mathworld.wolfram.com/ContinuedFractionConstants.html

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