show series is convergent or not by using subseries

Oct 2009
36
0
Aberystwyth, Wales
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.
 
Oct 2009
4,261
1,836
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"...?

Tonio
 
May 2010
12
4
explain precisely

It will better to explain the problem you want to solve more precisely. Are you trying comparison test?