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If S(1),S(2),S(3),"…….",S(2n) are the sa...

If `S_(1),S_(2),S_(3),"…….",S_(2n)` are the same of infinite geometric series whose first terms are respectively `1 , 2, 3,"…….", 2n` and common ratio are respectively. `1/2, 1/3, '…..". (1)/(2n+1)`.Find the value of `S_(1)^(2) + S_(2)^(2) + "……" + S_(2n-1)^(2)`.

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The correct Answer is:
`(n(2n+1)(4n+1))/(3)-1`
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