sum of 5+1/(5+1/(5+1/(5+1/5......)))

5+1/(5+1/(5+1/(5+1/5.....)))
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1 Answer

Question: sum of 5+1/(5+1/(5+1/(5+1/5......)))

This is an infinite continued fraction. Write it as,

x = 5 + 1/(5 + 1/(5 + ...

Then,

x = 5 + 1/x

x^2 = 5x + 1

x^2 - 5x - 1= 0

Usnig the quadratic formula, and taking the positive square root only,

x = (5 + sqrt(25 + 4)/2

x = (5 + sqrt(29)/2 = 5.19258...

by Level 11 User (81.5k points)

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