If , then the value of…

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

If f(n)=∏i=2n−1log⁡i(i+1)f(n)=\prod_{i=2}^{n-1}\log_i(i+1), then the value of ∑k=1100f(2k)\sum_{k=1}^{100}f(2^k) equals (1) 5010 (2) 5050 (3) 5100 (4) 5049

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