Evaluate $\displaystyle 10^2+12^2+14^2+...+30^2$
I was able to evaluate it by using the calculator, ans is 4840. but how could i get a more mathematical approach by using the summation sign or something
$\displaystyle 10^2+12^2+14^2+...+30^2$
$\displaystyle (2*5)^2+(2*6)^2+(2*7)^2+...+(2*15)^2$
$\displaystyle 4(5^2 + 6^2 + 7^2 + ... + 15^2)$
$\displaystyle 4(1^2 + 2^2 + 3^2 + ... + 15^2) - 4(1^2 + 2^2 + 3^2 + 4^2)$
So basically, we're factoring out the common 4, then writing is as the sum of the first n (15) squares, minus ... 4(1 + 4 + 9 + 16) = 120.