Question

The value of $\frac{2\frac{1}{2}}{1!} + \frac{3\frac{1}{2}}{2!} + \frac{4\frac{1}{2}}{3!} + \frac{5\frac{1}{2}}{4!} + ......\infty$ is.

• A. $1 + e$
• B. $\frac{1 + e}{e}$
• C. $\frac{e - 1}{e}$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

The series is

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

$= \left\{ \frac { 2 } { 1 ! } + \frac { 3 } { 2 ! } + \ldots . + \frac { n + 1 } { n ! } + \ldots \infty \right\} +$ $\frac{x}{1 + x} + \log_{e}(1 - x)$

$\frac{x}{1 - x} - \log_{e}(1 - x)$.