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Find the sum of series 1^2+3^2+5^2+…………………………..+11^2.(a) 279(b) 286(c) 309(d) 409The question was asked in final exam.This intriguing question comes from Sum to n Terms of Special Series in division Sequences and Series of Mathematics – Class 11

Answer» RIGHT choice is (b) 286

Explanation: 1^2+3^2+5^2+…………………………..+11^2

= (1^2+2^2+3^2+……+11^2) – (2^2+4^2+6^2+8^2+10^2)

= (1^2+2^2+3^2+……11^2) – 2^2(1^2+2^2+3^2+4^2+5^2)

= 11*12*23/6 – 4*5*6*11/6

= 506 – 220

= 286.


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