Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2004 | May-Jun | (P1-9709/01) | Q#4

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Question

Find the coefficient of in the expansion of

i. ii. Solution

i.

Expression for the general term in the Binomial expansion of is: In the given case: Hence;  Since we are looking for the term with , we can  equate  Finally substituting in:      Therefore the coefficient of is .

ii.

To find the coefficient of in the expansion of First of all we must notice that there will be two terms with . One is product of 1 from and from the expansion of . Second will be product of from and from the expansion of .

Therefore we look for the terms containing & in the expansion of We know that expression for the general term in the Binomial expansion of is: In the given case: Hence;  Since we are looking for the term with , we can  equate  Finally substituting in:      Therefore the term with is .

From (i) the term with is :

Therefore can be expanded in a limited way as:   Therefore, the coefficient of is .