determin whether the following geometric series converges or diverges. if the series converges find its sumSum(upper^infinity, lower n=0)…

determin whether the following geometric series converges or diverges. if the series converges find its sumSum(upper^infinity, lower n=0)…

determin whether the following geometric series converges or diverges. if the series converges find its sumSum(upper^infinity, lower n=0)…

We are asked if the geometric series `sum_0^(oo) (2^(2n))/(3^(n-1))` converges or diverges.We will use properties of exponents to rewrite:`sum_0^(oo) (2^(2n))/(3^(n-1))=sum_0^(oo)1/(3^(-1))(2^(2n))/(3^n)` `=sum_0^(oo)3(4^n/3^n)` `=sum_0^(oo)3(4/3)^n` The common ratio is `4/3>1` , so the series diverges.