Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2016  FebMar  (P19709/12)  Q#1
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Question
i. Find the coefficients of and in the expansion of .
ii. It is given that, when is expanded, there is no term in . Find the value of the constant .
Solution
i.
Expression for the general term in the Binomial expansion of is:
First we rewrite the expression in the standard form;
In the given case:
Hence;
Since we are looking for the terms with : we can equate




Now we can find the two terms with ;
Substituting ; 
Substituting ; 














Hence the coefficients of in the expansion of are & respectively.
ii.
It is evident that that coefficient of the term containing in the product of is zero.
We have found in (i) that in the expansion of we have terms;


Therefore can be written for terms containing as follows;
It can be expanded as;
As per given condition coefficient of the term containing is zero, therefore;
Hence;
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