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InterviewSolution
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Number of positive terms in the sequence `x_n=195/(4P_n)-(n+3p_3)/(P_(n+1)), n in N` (here `p_n=|anglen`) |
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Answer» Correct Answer - 4 We have, `x_(n)=(195)/(4P_(n))-(.^(n+3)A_(3))/(P_(n+1))` `thereforex_(n)=(195)/(4*n!)-((n+3)(n+2)(n+1))/((n+1)!)` `=-(195)/(4*n!)-((n+3)(n+2))/(n!)` `=(195-4n^(2)-20n-24)/(4*n!)=(171-4n^(2)-20n)/(4*n!)` `becausex_(n)` is positive `therefore(171-4n^(2)-20n)/(4*n!) gt0` `implies4n^(2)+20n-171 lt0` which is true for n=1,2,3,4 Hence, the given sequence `(x_(n))` has 4 positive terms. |
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