I have a question to show if the following series is convergent or not \(\displaystyle \Sigma_{n \rightarrow 0}^{\inf} \frac{7^{n+1}}{8^n}\)

and i have to show it with using different subseries most questions like this im ok with but with this im stumped would be very grateful for any help. Thanks.

I have a question to show if the following series is convergent or not \(\displaystyle \Sigma_{n \rightarrow 0}^{\inf} \frac{7^{n+1}}{8^n}\)

and i have to show it with using different subseries most questions like this im ok with but with this im stumped would be very grateful for any help. Thanks.

What do you mean "by subseries"?? The series is clearly convergent: \(\displaystyle \sum^\infty_{n=0}\frac{7^{n+1}}{8}=7\sum^\infty_{n=1}\left(\frac{7}{8}\right)^n\) , but what is "by subseries"...?