Determine whether the series $\backslash$infty $32$n$22$n $7$ n $=1$ converges or diverges. Solution For large n the dominant term in the denominator is $2$n$2,$ so we compare the given series with the series $3(2$n$2).$ Observe that $32$n$22$n $732$n$2$ because the left side has a bigger denominator. $($In the notation of the Comparison Test, an is the left side and bn is the right side.$)$ We know that $\backslash$infty $32$n$2$ n $=1=\backslash$infty $1$ n$2,$ n $=1$ which is convergent because it's a constant times a p$-$series with p $=>1.$ Therefore $\backslash$infty $32$n$22$n $7$ n $=1$ is by the Comparison Test.