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

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