Question: $\frac{1^{2}.2}{1!} + \frac{2^{2}.3}{2!} + \frac{3^{2}.4}{3!} + .....\infty =$\]...

Question

$\frac{1^{2}.2}{1!} + \frac{2^{2}.3}{2!} + \frac{3^{2}.4}{3!} + .....\infty =$ ]

Answer 1

$\frac{(\log 3)^{3}}{6}$

Here $\frac{3}{3!}$

$\frac{2}{1}.\frac{1}{3} + \frac{3}{2}.\frac{1}{9} + \frac{4}{3}.\frac{1}{27} + \frac{5}{4}.\frac{1}{81} + ......\infty =$

$\frac{1}{2} - \log_{e}\frac{2}{3}$

$- \log_{e}\frac{2}{3}$ .

Question: \(\frac{1^{2}.2}{1!} + \frac{2^{2}.3}{2!} + \frac{3^{2}.4}{3!} + .....\infty =\)\]...