+279 Given \(a_n=1/(n(n+1)(n+1))\), calculate \(a_1+a_2+...+a_n\)'s value.
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).
