Ta có : $2^2$ $= 4 = 4 . 1 = 4 . $ $1^2$
$4^2$ $= 16 = 4 . 4 = 4 .$ $2^2$
$6^2$ $= 36 = 4 . 9 = 4 .$ $3^2$
...................................................................
$20^2$ = 400 = 4 . 100 = 4 . $10^2$
Theo như trên thì ta có tổng :
$2^2$ + $4^2$ + $6^2$ + ..... + $20^2$ = 4 . ( $1^2$ + $2^2$ + $3^2$ + $10^2$ )
Mà : $1^2$ + $2^2$ + $3^2$ + $10^2$ = 506
=> $2^2$ + $4^2$ + $6^2$ + ..... + $20^2$ = 4 . 506
=> $2^2$ + $4^2$ + $6^2$ + ..... + $20^2$ = 2024
Vậy : $2^2$ + $4^2$ + $6^2$ + ..... + $20^2$ = 2024
