Question

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

• A. 2e
• B. 3 e
• C. 4 e
• D. 5 e

Answer 1

Answer: (D)

5 e

Answer 2

$S = \frac{1^{3}}{1!} + \frac{2^{3}}{2!} + \frac{3^{3}}{3!} + ........ + \frac{n^{3}}{n!} + ........$Here $T_{n} = \frac{n^{3}}{n!}$ ⇒

$S_{n} = \sum_{n = 1}^{\infty}{\frac{n^{3}}{n!} = 5e}$