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JEE Advanced Mathematics question

MathematicsSequence and SeriesJEE Advanced

If then is equal to

Answer: (C)

Solution

(The summation index is meant to be a dummy variable, say , running from 1 to .) The -th term is

Missing argument for \frac\frac{1+2+\dots+2^{k-1}}{

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Question ID VK-107848