I can do a, b, c and d alright, but I'm stuck on e.(a) Write down the Maclaurin series for . What it it's radius of convergence?
(b) Write down the Maclaurin series for
(c) Use (b) to find the Maclaurin series for f(x) = ln (1+x)
(d) What is the radius of convergence found in (c)?
(e) What is the interval of convergence found in (c)?
The radius of convergence is 1 (It's a geometric series where x is the ratio).
(d) The radius of convergence is still 1, integrating does not alter the radius of convergence.
Now how do I go about checking the interval of convergence? Is it just (-1, 1)?