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

 Jul 28, 2018
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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).

 Jul 28, 2018
edited by Guest  Jul 28, 2018

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