Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2008 | May-Jun | (P1-9709/01) | Q#3

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Question


i.       
Find the first three terms in the expansion, in ascending powers of , of in ascending powers of .

   ii.       Hence find the coefficient of  in the expansion of .

Solution


i.
 

Expression for the Binomial expansion of  is:

In the given case:

Hence;


ii.
 

To find the coefficient of  in the expansion of 

From (i) we have;

Therefore;

We are interested only in coefficient of terms with :

The only terms with :

Hence coefficient of  is .

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