# 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

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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;       