# Math Help - convergence of cesaro averages

1. ## 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?

2. 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

$\chi$ $\sigma$