5.17 Functions expressed as power series
Functions expressed as power series
Lessons
Notes:
Note *A formula that may be of use when expressing functions into power series:
$\frac{1}{1r}=\sum_{n=0}^{\infty}r^n$ knowing that $1$ < $r$ < $1$
When finding the interval of convergence, there is no need to check the endpoints. This is because the sum of the geometric series strictly converges only when $1$ < $r$ < $1$, and not at $r=1$.
If the function $f(x)$ has a radius of convergence of $R$, then the derivative and the antiderivative of $f(x)$ also has a radius of convergence of $R$.

1.
Expressing Functions as Power Series
Express the following functions as power series, and then find the interval of convergence: