Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2011 | Oct-Nov | (P1-9709/12) | Q#1

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Question

     i.       Find the first 3 terms in the expansion of , in ascending powers of .

   ii.       Use the result in part (i) to find the coefficient of  in the expansion of  .

Solution


i.
 

First rewrite the given expression in standard form.

Expression for the Binomial expansion of  is:

In the given case:

Hence;


ii.
 

We can rearrange/rewrite  as:

Where

We know from (i) that

Therefore substitute:

Hence the coefficient of variable  is .

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