Question

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

Answer 1

A geometric series of first term `a` and common ratio `r` is divergent if `|r|>=1`, and convergent if `|r|<1`, in which case the sum is given by the formula `a/(1-r)`. In the present case `r=1/6` is less than 1 in absolute value, so that the series is convergent and its sum is `-5/(1-(1/6))=-6`. See Geometric Series