Taylor Series

what does 0! equal to?

equals 1

What is the general formula of the taylor series

What is the general formula of the Maclaurin series

What is the power series of ln(1+x)

What is the power series of arctan(x)

What is the M.S for (1+ x) ^ 5, binomial series

If given a complicated fraction, what can you do to it to make it simplier?

Partial Fraction Decomposition (in terms like A, B, etc)

• Partial fractions —> often can use the telescoping technique to solve for conv or div

What fractions should you try to use telescoping technique on?

Fact

When building a power series, every x must be in the same format of (x-a)

• Cannot have a x randomly outside (x-a)

Fact

When trying to represent functions as power series, need to ask yourself if algebra application is in terms of overall x pattern

• e.g) can’t multiply x inside a (x-a) formatted equation —> sigma notation will be messed up