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If S (1), S (2) , S (3)……., S (2n) are t...

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