(22 + 42 + 62 + ... + 202) = ?

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Question

(2² + 4² + 6² + ... + 20²) = ?

Options:

A . 770

B . 1155

C . 1540

D . 385 x 385

Answer: Option C

(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.

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