Question

The value of $\sum _{r=0}^{10}{r}^{10}{C}_r{3}^r(-2{)}^{10-r}$ is

• A. 20
• B. 10
• C. 300
• D. 30

Answer 1

Answer: (D)

$\sum _{r=0}^{10}{r}^{10}{C}_r{3}^r(-2{)}^{10-r}$
$=10\sum _{r=0}^{10}{}^9{C}_{r-1}{3}^r(-2{)}^{10-r}$
$=10\times 3\sum _{r=0}^{10}{}^9{C}_{r-1}{3}^{r-1}(-2{)}^{10-r}$
$=30(3-2{)}^{10}$
$=30$