Question

Find the sum of the series
$3.{{}^{n}C}_0-8.{{}^{n}C}_1+{13.}^n{C}_2-18.{}^n{C}_3+\dots +(n+1)terms$

• A. $0$
• B. $-1$
• C. $+1$
• D. None of these

Answer 1

Answer: (A)

$0$

Let $n=2$
Hence the above expression is reduced to
$3\left(1\right)-8\left(2\right)+13\left(1\right)$
$=16-16=0$
Let $n=3$
$3\left(1\right)-8\left(3\right)+13\left(3\right)-18\left(1\right)$
$=42-42=0$
Hence the sum of the series for $n>1$ is $0$