A) 2K
B) k
C) k/2
D) 2048
Correct Answer: C
Solution :
\[\frac{1}{{{k}_{eff}}}=\frac{1}{k}+\frac{1}{2\,k}+\frac{1}{4\,k}+\frac{1}{8\,k}+....\] \[=\frac{1}{k}\left[ 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+..... \right]\]\[=\frac{1}{k}\left( \frac{1}{1-1/2} \right)\]\[=\frac{2}{k}\] (By using sum of infinite geometrical progression \[a+\frac{a}{r}+\frac{a}{{{r}^{2}}}+...\infty \] sum (S) \[=\frac{a}{1-r}\]) \[\therefore {{k}_{eff}}=\frac{k}{2}.\]
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