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Q.

If $S_{n}$ denotes the sum of the terms in the $n^{t h}$ bracket of the series $(1) + (3 + 5) + (7 + 9 + 11) + (13 + 15 + 17 + 19) + .......,$ then $(S_{11} - S_{9}) =$

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answer is 602.

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Detailed Solution

By observation $S_{n} = n^{3}$

$∴ S_{11} - S_{9} = 11^{3} - 9^{3} = 1331 - 729 = 602$

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If Sn denotes the sum of the terms in the nth bracket of the series (1)+(3+5)+(7+9+11)+(13+15+17+19)+......., then (S11−S9)=