 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-2/8/b/i/solution

Multiply the two power series and collect equal powers of

x

c_{0} = a_{0} b_{0}, c_{1} = a_{0} b_{1} + a_{1} b_{0}, c_{2} = a_{0} b_{2} + a_{1} b_{1} + a_{2} b_{0} .

Only terms whose two exponents add to the target exponent contribute.

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