InterviewSolution
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InterviewSolution
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The greatest term in the expansion of `(1 + 3X)^(54)` when ` x = (1)/(3)`,isA. `28^(th)`B. `25^(th)`C. `26^(th)`D. `24^(th)` |
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Answer» Correct Answer - a Let `T_(r +1) and T_(r)` denote the `(r +1)^(th) and r^(th)` terms respectively. Then `T_(r+1) = ""^(54)C_(r) (3x)^(r) and T_(r) = ""^(54)C_(r-1) (3x)^(r-1)` `therefore (T_(r+1))/(T_(r)) = (""^(54)C _(r))/(""^(54)C _(r-1))xx (3x)^(r) = (54 - r +1)/(r) xx(3x)^(r)` `rArr (T_(r+1))/(T_(r)) = (55-r)/(r) [because x = (1)/(3)]` Now,` (T_(r+1))/(T_(r)) gt 1 rArr (55-r)/(r) rArr r lt 27 (1)/(2)` Hence, `28 ^(th)` term is the greatest term. |
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