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If S(1), S(2), S(3),...S(n) are the sums...

If `S_(1), S_(2), S_(3),...S_(n)` are the sums of infinite geometric series, whose first terms are `1,2,3,...n` whose ratios are `(1)/(2),(1)/(3),(1)/(4) ,...(1)/(n+1)` respectively, then find the value of `S_(1)^(2)+S_(2)^(2)+S_(3)^(2)+...+S_(2n-1)^(2)`.

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The correct Answer is:
`(1)/(3)n(2n+1)(4n+1)-1`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
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