Question

how do i evaluate the sum of 〖10〗^2+〖12〗^(2 )+〖14〗^2+⋯+〖20〗^2. I tried using the difference method which gives n/6(n+1)(2n+2) but i can't seem to get it to work for this question.

Answer 1

[sum of squares from 1 to 20] minus [sum of squares from 1 to 9] =

[sum of squares from 10 to 20]

Answer 2

is there a formula to get the sum without manually summing each value in the series with the calculator?

Answer 3

yes... use the formula you gave: \(\huge \frac{n(n+1)(2n+1)}{6} \)

Answer 4

sum of squares from 1 to 20: \(\large \frac{(20)(20+1)(2*20+1)}{6} \)
sum of squares from 1 to 9 : \(\large \frac{(9)(9+1)(2*9+1)}{6} \)

Answer 5

i tried this method as well but the answer in my tutorial gives me 1420 instead of 2585.