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

Correct Answer: 1540

Explanation:

(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.

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