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Question

Question: \(C_{0} + 2C_{1} + 3C_{2} + .... + (n + 1)C_{n}\)term in the expansion of \((n + 2)2^{n - 1}\) is....

C0+2C1+3C2+....+(n+1)CnC_{0} + 2C_{1} + 3C_{2} + .... + (n + 1)C_{n}term in the expansion of (n+2)2n1(n + 2)2^{n - 1} is.

A

(n+1)2n1(n + 1)2^{n - 1}

B

(n+2)2n(n + 2)2^{n}

C

15C0215C12+15C22....15C15215C_{0}^{2} -^{15}C_{1}^{2} +^{15}C_{2}^{2} - .... -^{15}C_{15}^{2}

D

2C0+222C1+233C2+....+21111C102C_{0} + \frac{2^{2}}{2}C_{1} + \frac{2^{3}}{3}C_{2} + .... + \frac{2^{11}}{11}C_{10}

Answer

15C0215C12+15C22....15C15215C_{0}^{2} -^{15}C_{1}^{2} +^{15}C_{2}^{2} - .... -^{15}C_{15}^{2}

Explanation

Solution

Tr+1T_{r + 1}

0r550 \leq r \leq 55