Question

Help please?

Answer 1

The sum is `1185`

Explanation:

The number of terms in the expansion of `sum_(n)^k` is `k - n + 1`. Thus we will calculate the sum of `15 - 6 + 1 = 10` terms.

We now recall that the sum of the first `n` squares of integers is

`S_n = (n(n + 1)(2n + 1))/6`, where `n ≥ 1`

The sum of the first fifteen squares is

`S_15 = (15(16)(2(15) + 1))/6 = 1240`

But we must subtract the sum of the first five because `sum_(n = 1)^15 = sum_(n = 1)^6 + sum_(n = 6)^15`

`S_5 = (5(6)(2(5) + 1))/6 = 55`

Therefore

`sum_(n = 6)^15 = 1240 - 55 = 1185`

Hopefully this helps!