A geometric series is given by
[tex]\sum ^{\infty}_{n\mathop=0}a_1(r)^{n-1}[/tex]Where a1 represents the first term and r represents the common ratio.
The first term of our series is 8, and to find the common ratio we just need to divide one term by the previous one.
[tex]\frac{32}{8}=4[/tex]Our geometric series is
[tex]\sum ^{\infty}_{n\mathop{=}0}8(4)^{n-1}[/tex]A geometric series converges if and only if
[tex]-1the common ratio is within this range. Since 4 is not on this range, this series diverges.