Sequence And Series Question 561
Question: $ {\log_{e}}(1+x)=\sum\limits_{i=1}^{\infty }{
[ \frac{{{(-1)}^{i+1}}x^{i}}{i} ]} $ is defined for [Roorkee 1990]
Options:
A) $ x\in (-1,,1) $
B) Any positive (+) real x
C) $ x\in (-1,,1] $
D) Any positive (+) real $ x(x\ne 1) $
Show Answer
Answer:
Correct Answer: C
Solution:
$ {\log_{e}}(1+x)=\sum\limits_{i=1}^{\infty }{\frac{{{(-1)}^{i+1}}x^{i}}{i}} $ is defined for $ x\in (-1,1] $ Because $ {\log_{e}}(1+x)=x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-\frac{x^{4}}{4}+….\infty $ is defined for $ (-1<x\le 1) $ .
BETA
