Question

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

Answer 1

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`