SOLUTION: Σn=1 2/(n(n+1)) ITS AN INFINITE SERIES AND STARTS AT 1.

Question 1133418: Σn=1 2/(n(n+1))
ITS AN INFINITE SERIES AND STARTS AT 1.
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.


The requested sum is  (it is how I read the problem)


 +  +  + . . .  + . . . to infinity = 


        Each term   =  - .



        Therefore, any finite sum    +  +  + . . .  = 


        = ( - ) + ( - ) + ( - ) + . . . + ( - ) = all interior terms cancel each other, 


           and only two extreme (very first and very last) terms survive


         = 2 - .



It implies that the limit of the sum  at  n -->oo  is  2 (two, TWO).   ANSWER.

Solved.

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