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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- Feb 22nd 2010, 12:42 AMharish21convergence 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? - Feb 22nd 2010, 01:02 AMchisigma
Try to set...

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

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

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$