Question

How do you find the sum of the series `n^2` from n=0 to n=4?

Answer 1

`sum_(n=0)^4 n^2 = 30`

Explanation:

We need the standard formula `sum_(r=1)^n r^2=1/6n(n+1)(2n+1)`

`:. sum_(n=0)^4 n^2 = 1/6(4)(4+1)(8+1)`
`:. sum_(n=0)^4 n^2 = 1/6(4)(5)(9)`
`:. sum_(n=0)^4 n^2 = 30`

Alternatively, as there are only a few terms we could just write them out and compute the sum;
`sum_(n=0)^4 n^2 = 0^2 + 1^2 +2^2 + 3^2 + 4^2`
`:. sum_(n=0)^4 n^2 = 1 + 4 + 9 + 16`
`:. sum_(n=0)^4 n^2 = 30`, as before