# Introduction to Power Series

## Key Questions

• Taylor Series centered at c

f(x)=sum_{n=0}^infty {f^{(n)}(c)}/{n!}(x-c)^n

I hope that this was helpful.

• Useful Maclaurin Series

$\frac{1}{1 - x} = {\sum}_{n = 0}^{\infty} {x}^{n}$

e^x=sum_{n=0}^infty{x^n}/{n!}

sinx=sum_{n=0}^infty(-1)^n{x^{2n+1}}/{(2n+1)!}

cosx=sum_{n=0}^infty(-1)^n{x^{2n}}/{(2n)!}#

I hope that this was helpful.

• You can thing of a power series as a polynomial function of infinite degree since it looks like this:

${\sum}_{n = 0}^{\infty} {a}_{n} {x}^{n} = {a}_{0} + {a}_{1} x + {a}_{2} {x}^{2} + {a}_{3} {x}^{3} + \cdots$

I hope that this was sufficient.