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.
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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 $\displaystyle \sum_{n=0}^{\infty}2^nS_n=M$ The contra positive of the test for divergence we have that the limit $\displaystyle \lim_{n \to \infty}2^nS_n=0$ can you finish from here?
Yes it just clicked thank you
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