Expand power series of 1/(cosx) analytic at x=0. Find the first 4 terms of the series.
I know the taylor series for cosx, but isn't this just the same thing but with all the fractions flipped?
Lets suppose that the McLaurin expansion of exists and write...
(1)
In this case we can derive the from the McLaurin expansion of ...
(2)
... where for even and for odd. If we write the product of the series (1) and (2) we obtain...
(3)
... and from (3) we obtain...
The McLaurin expansion of with maximum exponent 4 is then...
(4)
Kind regards