Question

The sum of the series $1+2\times 3+3\times 5+4\times 7+\dots \text{upto}{11}^{\text{th}}\text{term}$ is :

• A. $916$
• B. $945$
• C. $946$
• D. $915$

Answer 1

The correct option is B $945$

Let $S=1+2\times 3+3\times 5+4\times 7+\dots \text{upto}{11}^{\text{th}}\text{term}$
General term of the above series is $n(2n-1)$
$\therefore S=\sum _{n=1}^{11}n(2n-1)$
$\Rightarrow S=2\sum _{n=1}^{11}{n}^2-\sum _{n=1}^{11}n$
$\Rightarrow S=2\times \frac{11\times 12\times 23}{6}-\frac{11\times 12}{2}$
or, $S=946$