ANS:C - 1540
(22 + 42 + 62 + ... + 202) = (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.