how do i find the mclaurin series for sec x?

Question

I dont know the method to solve this and there is no good web reference that shows me how to step by step solve this. I know what the terms need to look like, but i dont have a really good idea on the method. Can someone please help me, show me or refer me to something that clearly shows the method for working this out. My textbook only dedicates about 2 pages to mclaurin series :(

Best answer gets 10 points immediately

Answer 1

you differential sec(x) successively and substitute 0 for x

and substitute into the series

try the following link to see one method for finding 3 terms of the series

Answer 2

The expansion of sec(x) is given in equation 15 in the site below.
To derive it, you have to keep differentiating and plug in the values into equation 1.

y = sec(x)
y(0) = 1

y' = sec(x) tan(x)
y'(0) = 0

y" = secx tan^2 x + sec^3 x
y"(0) = 1

So far the expansion is: 1 + x^2 / 2 + ...
You just have to keep on differentiating and substituting x=0.

Answer 3

Try this http://en.wikipedia.org/wiki/Taylor_series

The MacLauren series is a variant of the Taylor series