Question

If $C_0,C_1,C_2,\dots ,C_{15}$ are the binomial coefficients in the expansion of $(1+x{)}^{15}$, then $\frac{C_1}{C_0}+\frac{2C_2}{C_1}+\frac{3C_3}{C_2}+\dots +\frac{15C_{15}}{C_{14}}$ is equal to

• A. 32
• B. 64
• C. 128
• D. None of these

Answer 1

Answer: (D)

$\frac{C_1}{C_0}+\frac{2C_2}{C_1}+\frac{3C_3}{C_2}+\dots +\frac{15C_{15}}{C_{14}}$
$=n+\frac{\frac{2n(n-1)}{2}}{n}+\frac{\frac{3n(n-1)(n-2)}{3\times 2}}{\frac{n(n-1)}{2}}+\dots$ upto $15$ terms
$=n+(n-1)+(n-2)+\dots +$ upto $15$ terms
$=\frac{15(15+1)}{2}=120$