Find the sum of the series _ r=0 ^ n (-1)^r ^n C_r 1 2^r + 3^r 2^ 2r + 7^r 2^ 3r +…

MATHEMATICS · Subjective · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

Find the sum of the series ∑r=0n(−1)rnCr{12r+3r22r+7r23r+15r24r+…upto m terms}.\sum_{r=0}^{n} (-1)^r {}^n C_r \left\{ \frac{1}{2^r} + \frac{3^r}{2^{2r}} + \frac{7^r}{2^{3r}} + \frac{15^r}{2^{4r}} + \dots \text{upto } m \text{ terms} \right\}.

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