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Calculus/maclaurin's series expansion

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Expert: - 10/7/2008


Question
in the maclaurin's series expansion of tan-1(x):
tan-1(x)=x – x3/3 +x5/5-.....;
the expansion is said to be valid only for |x|≤1.
why is this so?

thanks,
Aarthi

Answer
Because if x is greater than 1, there series won't hold.  For example, suppose x were 2.  It would b 2 - 8/3 + 32/5 - 128/7 + 512/9 - ...

Evaluating the terms, it can be seen that they increase.  The third term is >6.  The fourth term is < -18.  Keep going, they increase even faster.

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