11.9 Infinite Sequences & Series
Function Representation as Power Series
Question #1 (Easy): Representing Function Into Power Series
To convert the function into a power series, first think of geometric series whose sum iswhere a is
the constant first term and r the ratio. Since a can be taken to outside the summation, ultimately then,
the goal is to put into . Then given that geometric series converges for | , find the value for x
which in turn causes the “geometric series ratio” to be less than .