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...