Taylor expansion
Is there a shorter sweeter way to find expansion of sech(x) at x=0
http://www.wolframalpha.com/input/?i=expand+sechx+at+x%3D0

Question

Taylor expansion
Is there a shorter sweeter way to find expansion of sech(x) at x=0
http://www.wolframalpha.com/input/?i=expand+sechx+at+x%3D0

anonymous · Answer

I had this question on exam and it had options and I got it correct using calculator.
I think it would require at least half and hour calculating all those derivatives ... but the question had merely 10 min ... I am guessing there must really be shorter method to evaluate this as Taylor series.

anonymous · Answer

how accurate you want it?

anonymous · Answer

and I think you want maclurian series. It is special case where x=0 I think :)

anonymous · Answer

1-(1/2)*x^2+(5/24)*x^4+O(x^6)

anonymous · Answer

I think it is just memory and looking for a pattern

anonymous · Answer

I am guessing there must be short and sweet method ..
i want up to x^6

anonymous · Answer

Do you mean like a general formula? Look at the sixth section here: http://en.wikipedia.org/wiki/Hyperbolic_function It unfortunately doesn't seem to be analytic.

anonymous · Answer

oh ... yes it is.

anonymous · Answer

thanks ... what are these E's and B's??

anonymous · Answer

Oh .. Euler's number and Bernoulli's number ... 
don't have any idea ... anyway thanks a lot!!