frac{1}{2}-frac{1}{2 cdot 2^2}+frac{1}{3 cdot | vedclass

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(C) The given series is $\frac{1}{2}-\frac{1}{2 \cdot 2^2}+\frac{1}{3 \cdot 2^3}-\frac{1}{4 \cdot 2^4}+\ldots$ We know the logarithmic expansion $\log

Vedclass · Accepted Answer

$\log _e\left(\frac{3}{2}\right)$

Vedclass · Answer

(C) The given series is $\frac{1}{2}-\frac{1}{2 \cdot 2^2}+\frac{1}{3 \cdot 2^3}-\frac{1}{4 \cdot 2^4}+\ldots$ We know the logarithmic expansion $\log _e(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \ldots$ for $|x| Comparing the given series with the expansion,we can write it as $\frac{1}{2} - \frac{(1/2)^2}{2} + \frac{(1/2)^3}{3} - \frac{(1/2)^4}{4} + \ldots$ By substituting $x = \frac{1}{2}$ in the expansion,we get: $\log _e(1 + \frac{1}{2}) = \log _e(\frac{3}{2})$.

$\frac{1}{2}-\frac{1}{2 \cdot 2^2}+\frac{1}{3 \cdot 2^3}-\frac{1}{4 \cdot 2^4}+\ldots$ is equal to

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