Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | May-Jun | (P1-9709/12) | Q#3

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Question

     i.       Find the coefficients of  in the expansion of .

   ii.       Find the coefficient of  in the expansion of .

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 to get the terms containing  in the product of  we need;

This will result;

Hence we need first to find the terms with  and  i.e.  in the expansion of .

From (i) we have, in the expansion of ;

Since we are looking for the coefficient of .

Hence the coefficient of  is  .

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