How to determine the sum of the following series ?

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Answer 1 · 2018-07-08T14:17:03

# 0#.

Recall that, #sum_(m=1)^oo r^m=0, if, |r| lt 1#.

#:."The Reqd. Sum"=sum_(n=1)^00(-4)^(n-1)/6^n#,

#=sum{(-4)^n*(-4)^-1}/6^n#,

#=sum{(-4/6)^n*(1/-4)}#,

#=-1/4sum(-4/6)^n#,

#=-1/4(0)......[because, |r|=|-4/6|=2/3 lt 1]#,

#=0#.