# How do you find the maclaurin series expansion of #(x/(1+x^3))#?

Use the Maclaurin series for

#x/(1+x^3) = sum_(n=0)^oo (-1)^n x^(3n+1)#

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To find the Maclaurin series expansion of ( \frac{x}{1+x^3} ), we first express it as a geometric series. Then, we find the Maclaurin series expansion of the geometric series.

The Maclaurin series expansion of ( \frac{x}{1+x^3} ) is given by:

[ \frac{x}{1+x^3} = x(1 - x^3 + x^6 - x^9 + \ldots) ]

Expanding this series gives:

[ x - x^4 + x^7 - x^{10} + \ldots ]

So, the Maclaurin series expansion of ( \frac{x}{1+x^3} ) is ( x - x^4 + x^7 - x^{10} + \ldots )

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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