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