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Math Help - convergence of cesaro averages

  1. #1
    MHF Contributor harish21's Avatar
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    convergence of cesaro averages

    if the sequence {an} converges to a , and if we have a sequence defined as

    Sn = a1+a2+....+an / n

    then Sn also converges to a.

    how is that possible? isnt it supposed to be converged to 0?
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  2. #2
    MHF Contributor chisigma's Avatar
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    Try to set...

    a_{n} = a - b_{n} with \lim_{ n \rightarrow \infty} b_{n}=0 (1)

    ... the compute S_{n} as a function of the b_{n} and finally 'push' n to infinity...

    Kind regards

    \chi \sigma
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