The expansion $\log_e(1 + x) = \sum\limits_{i = 1}^\infty \left[ \frac{(-1)^{i + 1}x^i}{i} \right]$ is defined for:
- A$x \in (-1, 1)$
- BAny positive real $x$
- C$x \in (-1, 1]$
- DAny positive real $x$ where $x \neq 1$
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Similar Questions
If $0 < y < 2^{1/3}$ and $x(y^3 - 1) = 1$,then $\frac{2}{x} + \frac{2}{3x^3} + \frac{2}{5x^5} + \dots$ is equal to:
In the expansion of $\log_e \frac{1}{1 - x - x^2 + x^3}$,the coefficient of $x$ is
Medium
View SolutionIf $|x| < 1$ and $y = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \ldots$,then $x$ is equal to :
$\frac{(a - 1) - \frac{(a - 1)^2}{2} + \frac{(a - 1)^3}{3} - \dots \infty}{(b - 1) - \frac{(b - 1)^2}{2} + \frac{(b - 1)^3}{3} - \dots \infty} = $
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View SolutionLet $x \in R$ and $|x| < 1$. Then $\tanh ^{-1} x=$
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