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Math Help - Convergence of a series

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    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.
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    Quote Originally Posted by burdo View Post
    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?
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    Yes it just clicked thank you
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