Saturday, December 31, 2016

How to find the sum of this series?




The series is 112+214+318+




Or in other words



n=1n2n



What kind of series is this and how to find the sum? Thanks....


Answer



Without calculus:



If

s(a)=n=0nan
for
|a|<1,
then



as(a)=n=0nan+1=n=1(n1)an=n=1nann=1an=s(a)a1asos(a)=a(1a)2


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