Math 211-03

11-9-2017

* [Constructing power series]*

1. Construct the power series centered at for . Write your answer in summation form, or give the first 4 nonzero terms of the series. In addition, find the interval of convergence.

Let in the series for .

For the interval of convergence, I have . Since a square can't be negative, the relevant part of the inequality is . This gives , or .

2. Construct the power series centered at for . Write your answer in summation form, or give the first 4 nonzero terms of the series. In addition, find the interval of convergence.

Letting in the series for , I get

For the interval of convergence,

3. Construct the power series centered at for . Write your answer in summation form, or give the first 4 nonzero terms of the series. In addition, find the interval of convergence.

Letting in the series for , I get

For the interval of convergence,

4. Construct the power series centered at for . Write your answer in summation form, or give the first 4 nonzero terms of the series. In addition, find the interval of convergence.

Letting in the series for , I get

For the interval of convergence,

5. Construct the power series centered at for . Write your answer in summation form, or give the first 4 nonzero terms of the series. In addition, find the interval of convergence.

Letting in the series for , I get

For the interval of convergence,

6. Construct the power series centered at for . Write your answer in summation form, or give the first 4 nonzero terms of the series. In addition, find the interval of convergence.

Letting in the series for , I get

For the interval of convergence,

7. Construct the power series centered at for . Write your answer in summation form, or give the first 4 nonzero terms of the series. In addition, find the interval of convergence.

The series is centered at , so I want powers of .

Letting in the series for , I get

For the interval of convergence,

8. Find the function to which the power series converges.

Letting in the series for , I find that

9. Find the function to which the power series converges.

Letting in the series for , I find that

*Love is not consolation, it is light.* - *Simone Weil*

Copyright 2017 by Bruce Ikenaga