(2
2 + 4
2 + 6
2 + ... + 20
2 ) = (1 x 2)
2 + (2 x 2)
2 + (2 x 3)
2 + ... + (2 x 10)
2
= (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 102)
= 22 x [12 + 22 + 32 + ... + 102]
[ |
Ref: (12 + 22 + 32 + ... + n2) = |
1 |
n(n + 1)(2n + 1) |
] |
|
6 |
= |
❨ |
4 x |
1 |
x 10 x 11 x 21 |
❩ |
6 |
= (4 x 5 x 77)
= 1540.