01
Modifying geometric power series
Consider the geometric power series
for . For this problem, you should modify the series for
. (a) Write
as a power series centered at and determine its radius of convergence. (b) Write
as a power series centered at and determine its radius of convergence.
02
Power series of a derivative
Suppose that a function
has power series given by: The radius of convergence of this series is
. What is the power series of
and what is its radius of convergence?
03
Finding a power series
Find a power series representation for these functions:
(a)
(b)
04
Modifying and integrating a power series
(a) Modify the power series
for to obtain the power series for . (b) Now integrate this series to find the power series for
.