Find the sum of 1+frac{1}{2}+frac{1}{2^{2}}+f | vedclass

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(C) The given series is $1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \cdots$.This is an infinite geometric progression $(GP)$ where the firs

Vedclass · Accepted Answer

$2$

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(C) The given series is $1 + \frac{1}{2} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \cdots$.This is an infinite geometric progression $(GP)$ where the first term $a = 1$ and the common ratio $r = \frac{1}{2}$.The sum of an infinite $GP$ is given by the formula $S_{\infty} = \frac{a}{1-r}$,provided $|r| Here,$|r| = |\frac{1}{2}| Substituting the values,we get $S_{\infty} = \frac{1}{1 - \frac{1}{2}} = \frac{1}{\frac{1}{2}} = 2$.

Find the sum of $1+\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\cdots$ to infinite terms.

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