9231 P13 - Nov 2011 - Q2 - 6 marks
6556
Prove by mathematical induction that, for all positive integers \(n\),
\(\frac{\mathrm{d}^{n}}{\mathrm{~d} x^{n}}\left(\frac{1}{2 x+3}\right)=(-1)^{n} \frac{n!2^{n}}{(2 x+3)^{n+1}}\)
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