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The sum of the first 9 terms of the series `1^3/1 + (1^3 + 2^3)/(1+3) + (1^3 + 2^3 +3^3)/(1 + 3 +5)` ..... is :A. 142B. 192C. 71D. 96 |
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Answer» Correct Answer - D Let `T_(n) " be "n^(th)` term of the series. Then `T_(n)=(1^(3)+2^(3)+3^(3)+ . . . +n^(3))/(1+3+5 . . ..+(2n-1))=({(n(n+1))/(2)}^(2))/(n^(2))=(1)/(4)(n+1)^(2)` `:." Required sum"=underset(r=1)overset(9)sumT_(r)=underset(r=1)overset(9)sum(1)/(4)(r-1)^(2)` `=(1)/(4)(2^(2)+3^(2)+ . . . . +10^(2))` `=(1)/(4){(1^(2)+2^(2)+ . . . +10^(2))-1^(2)}` `=(1)/(4){(10(10+1)(20+1))/(6)-1}` `=(1)/(4)(384)=96` |
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