Question

$1 + \left( \frac{1}{2} + \frac{1}{3} \right)\frac{1}{4} + \left( \frac{1}{4} + \frac{1}{5} \right)\frac{1}{4^{2}} + \left( \frac{1}{6} + \frac{1}{7} \right)\frac{1}{4^{3}} + ....\infty =$

• A. $\log_{e}(2\sqrt{3})$
• B. $2\log_{e}2$
• C. $\log_{e}2$
• D. $\log_{e}\left( \frac{2}{\sqrt{3}} \right)$

Answer 1

Answer: (A)

$\log_{e}(2\sqrt{3})$

Answer 2

$\frac{e^{x} - e^{y}}{2}$

$1 + \frac{a - b}{a} + \frac{1}{2!}\left( \frac{a - b}{a} \right)^{2} + \frac{1}{3!}\left( \frac{a - b}{a} \right)^{3} + ......\infty =$

$x =$

$e^{a}$.