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Question: The value of 2C<sub>0</sub> + \(\frac{2^{2}}{2}C_{1}\)+ \(\frac{2^{3}}{3}C_{2}\)+ \(\frac{2^{4}}{4}C...

The value of 2C0 + 222C1\frac{2^{2}}{2}C_{1}+ 233C2\frac{2^{3}}{3}C_{2}+ 244C3\frac{2^{4}}{4}C_{3}+….+21111C10\frac{2^{11}}{11}C_{10} is –

A

311–111\frac{3^{11}–1}{11}

B

211–111\frac{2^{11}–1}{11}

C

113–111\frac{11^{3}–1}{11}

D

112–111\frac{11^{2}–1}{11}

Answer

311–111\frac{3^{11}–1}{11}

Explanation

Solution

aC0 + a22C1\frac{a^{2}}{2}C_{1}+ a33C2\frac{a^{3}}{3}C_{2}+…..+an+1n+1Cn\frac{a^{n + 1}}{n + 1}C_{n}

= (1+a)n+1–1n+1\frac{(1 + a)^{n + 1}–1}{n + 1}

Put a = 2 and n = 10