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  4. T he value of the sum S=(1/2)+(1/6)(12+22)+(1/12)(12+22+32)+(1/20)(12+22+32+42)+ ldots ldots .+(1/3660)(12+22+32+ ldots+602)

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Q. T he value of the sum $S=\frac{1}{2}+\frac{1}{6}\left(1^2+2^2\right)+\frac{1}{12}\left(1^2+2^2+3^2\right)+\frac{1}{20}\left(1^2+2^2+3^2+4^2\right)+\ldots \ldots .+\frac{1}{3660}\left(1^2+2^2+3^2+\ldots+60^2\right)$

Sequences and Series

Solution:

Correct answer is (a) 620