Question

Find the sum of the series $1+(1+2)+(1+2+3)+(1+2+3+4)+\cdots +(1+2+3+\cdots \cdots +20)$.

• A. 1470
• B. 1540
• C. 1610
• D. 1370

Answer 1

The correct option is B 1540

Consider the given series.

$1+(1+2)+(1+2+3)+(1+2+3+4)+...+(1+2+3+4+......+20)$

Here, $n=20$

We know that

$=\frac{n(n+1)(n+2)}{6}$

Put $n=20$, we get

$=\frac{20\left(21\right)\left(22\right)}{6}$

$=1540$

Hence, this is the answer.