What is the sum of the series?

Okay, the number above the sigma(4) indicates what value you go to, and what's below the sigma tells you where to start, and the stuff on the right is the expression you're using.

So we start with 1 and go to 4, adding all the values in between.

(2(1))^2 + (2(2))^2 + (2(3))^2 + (2(4))^2

2^2 + 4^2 + 6^2 + 8^2

4 + 16 + 36 + 64

120