Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2015 | Oct-Nov | (P1-9709/12) | Q#2

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Question

In the expansion of , where k is a non-zero constant, the coefficients of  and  are equal. Find the value of k.

Solution

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

We are given the expression for expansion as;

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 ;

We are given that the coefficients of  and  are equal.

Therefore;

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