Working with power series

What changes with the initial n value when you take the derivative of a power series

it becomes 1

What does not change when you take the derivative of aa power series

The radius of convergence

Would the derivative of this function increase the initial n value

no, because the 1st term (n=0) of the non-derivative function is X. And the derivative of X is 1, not 0.

When should you use tests to find the radius of convergence and when can you just set the magnitude of X less than 1

If there is only one n in the series equation you can just set the magnitude of x less than 1

If there are multiple n in the series equation you have to use one of the tests to simplify the equation

Where should the c go when solving integrals with a power series

on the left side of the series symbol

What must we remove after using integrals to solve for a power series problem

You must remove the “C” by solving for it

How do you solve for the actual value for “C” after using an integral to solve a power series

You sub in any number in the range of the convergence (most likely 0) into both sides of the series and then solve

When do you not have to solve for “C”

when there is an integral symbol on the left side of the equation

How can you find integrals for complicated functions

you set a part of the equation as u and then du is the derivative of u. You then try to organize the u and du to make it match the equation. Then you find the integral of the new equation.