power series expansion

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• Feb 5th 2009, 04:31 PM
mr_motivator
power series expansion
what is the coefficient of x^2 in the power series expansion of (4 + 7x)^(1/3)?
• Feb 5th 2009, 04:41 PM
bob murray
Try a Taylor expansion:

$f(x)=f(a)+(x-a)\frac{\partial}{\partial x} f(a) + \frac{(x-a)^{2}}{2!} \frac{\partial^{2}}{\partial x^{2}} f(a) + ...$

Use $a = 0$, and take the necessary derivatives. The third term in the above series is what you're looking for.