# Math Help - Convergence of a series

1. ## Convergence of a series

I have been asked to prove that Sn → 0 as n → , given that the series Σ2^n Sn is convergent. Any help would be really appreciated thanks.

2. Originally Posted by burdo
I have been asked to prove that Sn → 0 as n → , given that the series Σ2^n Sn is convergent. Any help would be really appreciated thanks.
Hint:

Since the series converges

$\sum_{n=0}^{\infty}2^nS_n=M$

The contra positive of the test for divergence we have that the limit

$\lim_{n \to \infty}2^nS_n=0$

can you finish from here?

3. Yes it just clicked thank you