Estimate the error, as a function of x, in approximating \[ ln(x+1) \] as \[x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4} \].
That is, what is \[ ln(x+1)- (x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}) \], or \[\frac{x^5}{5}-\frac{x^6}{6}+\frac{x^7}{7}..... \] expressed in a more compact form?

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this is alternating series ... the maximum error of nth order is given by |n+1 term|

So\[\frac{x^5}{5}-\frac{x^6}{6}+\frac{x^7}{7}..... \le |\frac{x^5}{5}| \]?

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