Question

The sum of the series $\frac{1^{2}}{1 \cdot 2!} + \frac{1^{2} + 2^{2}}{2 \cdot 3!} + \frac{1^{2} + 2^{2} + 3^{2}}{3 \cdot 4!} + .. + \frac{1^{2} + 2^{2} + ... + n^{2}}{n \cdot (n + 1)!} + ...\infty$

Equals.

• A. $e^{2}$
• B. $\frac{1}{2}(e + e^{- 1})^{2}$
• C. $\frac{3e - 1}{6}$
• D. $\frac{4e + 1}{6}$

Answer 1

Answer: (C)

$\frac{3e - 1}{6}$

Answer 2

$1 - \log_{e}2$

$\log_{3}e - \log_{9}e + \log_{27}e....$ = $\log_{3}2$

= $\log_{2}3$.