I can do a, b, c and d alright, but I'm stuck on e.(a) Write down the Maclaurin series for $\displaystyle \dfrac{1}{1-x}$. What it it's radius of convergence?

(b) Write down the Maclaurin series for $\displaystyle \dfrac{1}{1+x}$

(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)?

(a) $\displaystyle \dfrac{1}{1-x} = 1 + x + x^2 + x^3 + x^4 + x^5 ...$

The radius of convergence is 1 (It's a geometric series where x is the ratio).

(b) $\displaystyle \dfrac{1}{1+x} = 1 - x + x^2 - x^3 + x^4 - x^5 ...$

(c) $\displaystyle \displaystyle \int \dfrac{1}{1+x} = \ln (1+x) = x - \dfrac{x^2}{2} + \dfrac{x^3}{3} - \dfrac{x^4}{4} + \dfrac{x^5}{5} - \dfrac{x^6}{6} ...$

(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)?