# \(\infty\sum\) (i)

**Calculus**Level pending

\(\small Given\ the\ infinite\ sum: \) \(\small S= \frac{2^k}{1\cdot 2\cdot 3}+\frac{3^k}{2\cdot 3\cdot 4}+\frac{4^k}{3\cdot 4\cdot 5}+\cdots \)

\(\small For\ which\ k > 0\ values\ is\ this\ sum\ convergent\ or\ divergent,\ respectively? \)

\(\small a)\ k < 2\ \ and\ k\geq 2\\\small b)\ k < 2\ \ and\ k\geq 3\\\small c)\ k < 1\ \ and\ k\geq 3\\\small d)\ k < 0\ \ and\ k\geq 0\ \)

\(\small Note: There\ is\ a\ criteria\ which\ allows\ you\ finish\ in\ less\ than\ a\ minute\)