1.The sum of the series ∑r=0n(−1)rr⋅nCr(12r+3r22r+7r23r+15r24r+… m terms)\sum_{r=0}^{n} (-1)^{r} r \cdot {}^nC_{r} \left( \frac{1}{2^{r}} + \frac{3^{r}}{2^{2r}} + \frac{7^{r}}{2^{3r}} + \frac{15^{r}}{2^{4r}} + \ldots \text{ m terms} \right)∑r=0n(−1)rr⋅nCr(2r1+22r3r+23r7r+24r15r+… m terms) isa.2mn−12mn(2n−1)\frac{2^{mn}-1}{2^{mn}(2^{n}-1)}2mn(2n−1)2mn−1b.2mn−12n−1\frac{2^{mn}-1}{2^{n}-1}2n−12mn−1c.2mn+12n+1\frac{2^{mn}+1}{2^{n}+1}2n+12mn+1d.None of theseLogin to continueOnly logged in users canattempt or see the solution.
