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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]

 (22 + 42 + 62 + ... + 202) = ?  Ref: (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1)  (22 + 42 + 62 + ... + 202) = ?      6

=  (22 + 42 + 62 + ... + 202) = ?  4 x 1 x 10 x 11 x 21  (22 + 42 + 62 + ... + 202) = ?  6

= (4 x 5 x 77)

= 1540.



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