I need to determine the smallest value m, such that:

$$ \left |\int_0^{0.1} arctan(x^2) dx - \sum_{n=0}^m (-1)^n \frac{(0.1)^{(4n+3)}}{(4n+3)(2n+1)} \right| < 10^{-8} $$

Using the Alternate Series Test.

Unfortunately, I have no idea where to start for this.

The example (http://archives.math.utk.edu/visual.calculus/6/series.10/5.html) I looked at seemed to ignore the summation, and then solve for (m+1) but I'm not sure why that would work...



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