If f:R→R be a differentiable function at x=0 satisfying f(0)=0 and f'(0)=2, then the value of limr→01r∑n=1∞(−1)nfrnis

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−loge2

−2loge2

answer is C.

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Detailed Solution

limr→01r∑n=1∞(−1)nfrn=limr→0∑n=1∞(−1)nfrnr=limr→0∑n=1∞(−1)n1nf'rn1=∑n=1∞(−1)n1nf'01=limr→0∑n=1∞(−1)n2n=−2limr→0∑n=1∞(−1)n−1n=−2loge2

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