queries about convergence Can anyone help me with the proof that $a_n=\sum_{i=0}^{n}\frac{1}{n\choose i}$ converges.Now involving that I have two questions.Firstly is there a closed formula for $a_n$?And secondly is the general series convergent?
$a_{n,s}=\sum_{i=0}^{n}\frac{1}{{n\choose i}^s}$.

The general series {$a_{n,s}$} is not convergent, at least not for all $s$; for $s=1$, it will not, because :
$a_n=\sum_{i=0}^{n}\frac{1}{n\choose i}$  will contain ${n\choose 0}={n\choose 1}=1$ , so that $a_n >2 $ for all $n$
