Question

1²+3²+5²+7².....+19²=?

Answer 1

use the scientific calculator

Answer 2

Hello,

$1^2+3^2+5^2+...+19^2\\ =(2*0+1)^2+(2*1+1)^2+(2*2+1)^2+...+(2*9+1)^2=\sum_{i=0}^9(2*i+1)^2\\ =[(2*0)^2+1^2+2*2*0]+[(2*1)^2+1^2+2*2*1]+[(2*2)^2+1^2+2*2*2]+...+[(2*9)^2+1^2+2*2*9]\\ =4(0^2+1^2+3^2+...+9^2)+1+1+1+...+1+4(0+1+2+3+..+9)\\ =4*\dfrac{9*10*19}{6}+10+4*\dfrac{9*10}{2}\\ =60*19+10+180\\ =1330$