Even powers and a general term

Even powers and a general term

IB Year 5 | Grade 11
7 marks

Expand \((9+x^2)^{-2}\) up to and including the term in \(x^6\). State its open range of validity and the coefficient of \(x^{2r}\) for an integer \(r\ge0\).[7]

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Answer:\(\frac1{81}-\frac2{729}x^2+\frac1{2187}x^4-\frac4{59049}x^6+\cdots;\ |x|<3;\ \frac{(-1)^r(r+1)}{9^{r+2}}\)

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