Question

The value of $\sum _{r=1}^{10}r\cdot \frac{{}^n{C}_r}{{}^n{C}_{r-1}}$ is equal to

• A. $5(2n-9)$
• B. $10n$
• C. $9(n-4)$
• D. none of these

Answer 1

Answer: (A)

$\sum _{r=1}^{10}r\cdot \frac{{}^n{C}_r}{{}^n{C}_{r-1}}=\sum _{r=1}^{10}(n-r+1)$
$=(n+1)\times 10-\frac{10\times 11}{2}=10n-45$