Question

What is the value of the summation `sum_(i=1)^4(2i + 6i^2)`?

Answer 1

`\sum_{i=1}^4 (2i+6i^2)=200`

Explanation:

Given we have to solve `\sum_{i=1}^4 (2i+6i^2)`

We have to first break open the sum into 2 parts, which will be
`2\sum_{i=1}^4(i)+6\sum_{i=1}^4(i^2)`
Since both `2` and `6` in their respective terms are constants that do not change, I've kept them out of the sum term.

Now, the question is easy.
Of course we know that `\sum_{i=1}^ni=n(n+1)/2` and that `\sum_{i=1}^ni^2=n(n+1)(2n+1)/6`
So substituting `n=4`, we get `\sum_{i=1}^4i=cancel{4}^2*5/cancel{2}=10` and `\sum_{i=1}^ni^2=cancel{4}^2*5*cancel{9}^3/cancel{6}^1=30`

Taking all that into their respective places, you'll see what the answer is.