If then,
Integrate both side from where to get,
Now this hold if .
But it also hold when .
That is a little more difficult to show.
how could i expand something such as arctan'x (derivate of arctanx ... i.e. d/dx arctanx) into a power series. also how would you be able to find the radius of convergence for it?
so far i have managed to work out that:
arctan'x =
how do you work out the "radius of convergence" though: i know it is : |x|< 1.. but how do you work it out please?
i tried it on
i ended up with
as n tends to infinity... ...
so radius of convergence is |x|< 1...
is this working out correct?