We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
128
1
avatar+283 

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

 Jul 28, 2018
 #1
avatar
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).

 Jul 28, 2018
edited by Guest  Jul 28, 2018

13 Online Users

avatar
avatar
avatar