Question

If $(1 + x)^{n} = C_{0} + C_{1}x + C_{2}x^{2} + ....... + C_{n}x^{n}$, then the value of $C_{0} + 2C_{1} + 3C_{2} + ......(n + 1)C_{n}$ will be

• A. $(n + 2)2^{n - 1}$
• B. $(n + 1)2^{n}$
• C. $(n + 1)2^{n - 1}$
• D. $(n + 2)2^{n}$

Answer 1

Answer: (A)

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

Answer 2

Sol. Trick: Put $n = 1$ the expansion is equivalent to $1 ⥂ C_{0} + 2.^{1}C_{1} = 1 + 2 = 3$.

Which is given by option (1) = $(n + 2)2^{n - 1}$ =$(1 + 2)2^{0} = 3$