Question

4+16+36+64+...+10000

Answer 1

Ta có 4+16+36+64+...+10000

=22+42+62+82+...+1002

Ta có công thức tổng quát

22+42+62+...+(2n)2=2n(n+1)(2n+1)6\frac{2n\left(n+1\right)\left(2n+1\right)}{6}62n(n+1)(2n+1)​

Ta có 100=2x50

Vậy 22+42+62+82+...+1002=4+16+36+64+...+10000=2x50x(50+1)(2x50+1)6=2x50x51x1016=85850\frac{2x50x\left(50+1\right)\left(2x50+1\right)}{6}=\frac{2x50x51x101}{6}=8585062x50x(50+1)(2x50+1)​=62x50x51x101​=85850

Answer 2

1*1+3*3+5*5+7*7+...+99*99