Question

$\sum _{r=0}^{63}\frac{{}^n{C}_r}{{}^n{C}_r+{}^n{C}_{r+1}}$ is equal to (where $n=64$ )

• A. 60
• B. 64
• C. 35
• D. 32

Answer 1

Answer: (D)

$\sum _{r=0}^{63}\frac{{}^n{C}_r}{{}^{n+1}{C}_{r+1}}=\sum _{r=0}^{63}\frac{r+1}{n+1}=\frac{1}{n+1}(1+2+3\dots \dots 64)$ $=\frac{1}{65}\times \left(\frac{64\times 65}{2}\right)=32$.