Question

How do I find the sum of the infinite geometric series such that `a_1=-5` and `r=1/6`?

Answer 1

For the infinite geometric series `S=a_1+a_1r+a_1r^2+cdots` we can use the formula `S=a_1/(1-r)` as long as `|r|<1`.

In our case, `a_1=-5, r=1/6` and `|r|=|1/6|=1/6<1` so
`S=(-5)/(1-1/6)=(-5)/(5/6)=-5* 6/5=-6`