Question

What is the sum of the series *picture attached*

Answer 1

`\sum_(n=4)^(18)(n+1)^2=2440`

Explanation:

Series:
`\sum_(n=4)^(18) (n+1)^2`

Formula :
`\sum_(k=m)^n=\sum_(k=1)^n-\sum_(k=1)^(m-1)`

`\Rightarrow \sum_(n=4)^(18)(n+1)^2=\sum_(n=1)^(18)(n+1)^2-\sum_(n=1)^(3)(n+1)^2`

`\sum_(n=1)^(18)(n+1)^2=2469`

`\sum_(n=1)^(3)(n+1)^2=29`

`\Rightarrow \sum_(n=4)^(18)(n+1)^2=2469-29`

`\Rightarrow \sum_(n=4)^(18)(n+1)^2=2440`

So, Option C is true