JEE Advance - Mathematics (1991 - No. 11)
If $${S_1}$$, $${S_2}$$, $${S_3}$$,.............,$${S_n}$$ are the sums of infinite geometric series whose first terms are 1, 2, 3, ...................,n and whose common ratios are $${1 \over 2}$$, $${1 \over 3}$$, $${1 \over 4}$$,....................$$\,{1 \over {n + 1}}$$ respectively, then find the values of $${S_1}^2 + {S_2}^2 + {S_3}^2 + ....... + {S^2}_{2n - 1}$$
${{{}^n(n + 1),(2n + 1) - 3} \over 3}$
${{{}^n(n + 1),(4n + 1) - 3} \over 3}$
${{{}^n(2n + 1),(4n + 1) - 3} \over 3}$
${{{}^n(2n + 1),(2n + 1) - 3} \over 3}$
${{{}^n(3n + 1),(4n + 1) - 3} \over 3}$
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