Question

How do you use the properties of summation to evaluate the sum of `Sigma (i^2+3)` from i=1 to 20?

Answer 1

`sum_(i=1)^20(i^2+3) = 2930`

Explanation:

You can use the standard result

`sum_(i=1)^ni^2=1/6n(n+1)(2n+1)`

So:

`sum_(i=1)^20(i^2+3) = sum_(i=1)^20(i^2)+ sum_(i=1)^20(3)`
`:. sum_(i=1)^20(i^2+3) = 1/6(20)(21)(41)+(20)(3)`
`:. sum_(i=1)^20(i^2+3) = 2870+60`
`:. sum_(i=1)^20(i^2+3) = 2930`