\[\frac{1}{x + 1} + \frac{1}{2(x + 1)^{2}} + \frac{1}{3(x +... | MATH - LOGARITHMIC SERIES | SolveeIt | Solveeit

Today, August 18

Question

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

A

$\log_{e}\left( 1 + \frac{1}{x} \right)$

B

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

C

$\log_{e}\left( \frac{x}{x + 1} \right)$

D

None of these

Answer

$\log_{e}\left( 1 + \frac{1}{x} \right)$

Explanation

Solution

Given series is

$y = x - \frac{x^{2}}{2!} + \frac{x^{3}}{3!} - \frac{x^{4}}{4!} + ......,$

$x =$

$\log_{e}(1 - y)$ .