# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#2

Question

The coefficient of  in the expansion of  is 100. Find the value of the constant  a.

Solution

We can find the coefficient of  in the expansion of given expression by finding coefficients of  in  the expansion of individual terms of expression and then adding them.

Let us first find the coefficient of  in the expansion of .

We are given expression as;

Expression for the general term in the Binomial expansion of  is:

First rewrite the given expression in standard form.

In the given case:

Hence;

Since we are looking for the terms with  i.e. : we can  equate;

Now we can find the term with; Substituting ;

Hence the coefficient of   is .

Now we find the coefficient of  in the expansion of .

We are given expression as;

Expression for the general term in the Binomial expansion of  is:

In the given case:

Hence;

Since we are looking for the terms with  i.e. : we can  equate;

Now we can find the term with; Substituting ;

Hence the coefficient of   is .

Therefore, coefficient of  in the expansion of  is;

We are given that coefficient of  in the expansion of  is 100;