How do you find the sum of the infinite geometric series, a(1)= -5, r= 1/6?

1 Answer
Shwetank Mauria
Mar 24, 2016

Sum of infinite series is -6

Explanation:

Sum of geometric series {a,ar,ar^2,ar^3,,,,,,,,,,} up to n terms is given by

S=axx(r^n-1)/(r-1) if r>0 and

S=axx(1-r^n)/(1-r) if r<0

If r<0, Lt_(n->oo)(r^n)=0 and hence S=a/(1-r)

Here as a=-5 and r=1/6 and as r<1

S=-5/(1-1/6)=-5/(5/6)=-5xx6/5=-6

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