Question

Which option is correct and how would one solve for it?

Answer 1

28

Explanation:

We need to find the value of
`\Sigma_(x=0)^3\ 2x^2`

We know that,

`\Sigma n^2=(n(n+1)(2n+1))/(6)`

Here, n = 3

So,

`\Sigma n^2=(3(3+1)(2(3)+1))/(6)\\\\\Sigma n^2=14`

So,

`\Sigma_(x=0)^3\ 2x^2=2* 14\\\\=28`

So, the value of
`\Sigma_(x=0)^3\ 2x^2` is 28. Hence, the correct option is (d).