Question

$\frac{{}_{C_0}}{1}+\frac{{}_{C_1}}{2}+\frac{{}_{C_2}}{3}+\cdot \cdot \cdot \cdot +\frac{{}_{C_{10}}}{11}$ is equal to (here $C_r{=}^{10}{C}_r$)

• A. $\frac{2^{11}}{11}$
• B. $\frac{2^{11}-1}{11}$
• C. $\frac{3^{11}}{11}$
• D. $\frac{3^{11}-1}{11}$

Answer 1

The correct option is B $\frac{2^{11}-1}{11}$

Applying integration formula to $(1+x{)}^n$ and substituting x=1, we get
$\frac{(2{)}^{n+1}-1}{n+1}$
In the above case $n=10$.
Hence
Substituting n=10, we get
$\frac{2^{11}-1}{11}$.