Given \(a_n=1/(n(n+1)(n+1))\), calculate \(a_1+a_2+...+a_n\)'s value.

yasbib555 Jul 28, 2018

#1**0 **

I think this is the golden ratio (sqrt(5) + 1) / 2 represented as "continued fraction" as follows:

1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + **1/a(n)**))))))))))))))))))))))=**Sqrt(5).**

Guest Jul 28, 2018

edited by
Guest
Jul 28, 2018