InterviewSolution
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InterviewSolution
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Find the negative terms of the sequence `X_(n)=(.^(n+4)P_(4))/(P_(n+2))-(143)/(4P_(n))` |
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Answer» We have, `x_(n)=(.^(n+4)P_(4))/(P_(n+2))-(143)/(4P_(n))` `thereforex_(n)=((n+4)(n+3)(n+2)(n+1))/((n+2)!)-(143)/(4n!)` `=((n+4)(n+3)(n+2)(n+1))/((n+2)(n+1)n!)-(143)/(4n!)` `=((n+4)(n+3))/(n!)-(143)/(4n!)=((4n^(2)+28n-95))/(4n!)` `because x_(n)` is negative `therefore((4n^(2)+28n-95))/(4n!) lt 0` which is true for n=1,2. Hence, `x_(1)=(63)/(4) and x_(2)=-(23)/(8)` are two negative terms. |
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