8.9: Finding Power Series Using Algebra or Calculus Many times a function does not have a simple way to rewrite as the sum of an infinite geometric series. Many functions can be manipulated using algebra or calculus to resemble an “easier” power series.

Using an “Easier” Power Series

Combining Two “Easier” Power Series

Using Calculus Sometimes a function can be thought of as the derivative or an integral of a function that has an “easy” power series. Find the derivative or integral of the “easier” power series and use that to represent the original function.

Using Differentiation

Using Integration