To find Convergence/Divergence of
$\displaystyle u(n) = \sum \frac{1}{n!}$
and of this one
$\displaystyle u(n) =\sum \frac{1.2.3.4.5.6.....}{1.3.5.7.9......} $
Thank you.
You should write $\displaystyle u(n)=\frac 1{n!}$ for the first, not for the whole sum since it won't depend on $\displaystyle n$. Use the fact that $\displaystyle n!\geq n(n-1)$. For the second, could you write the terms with a formula on which $\displaystyle n$ appears?