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euler's foiler

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need help - maclaurin series?

Ok, I've memorised the maclaurin series for sin(x) and cos(x), but what is the pattern for tan(x)?

I just can't see what the pattern is. Can someone help? Like, for sin(x), the denominator is 3!, than 5!, then 7!, etc... and for cos it's 2!, then 4!, then 6!, etc... but for tan(x), it goes 3, then 15, then 315, then 2835?? what the hell? I cant find any help ANYWHERE, the closest I've found is "the pattern is hard to spot" but that is no help at all -_- I know tan(x) = sin(x)/cos(x), but I am still confused because the numerators of the tan(x)  maclaurin series make no sense to me either! 1, 2, 17, 62... I see no pattern! help!

i'm begging you... you don't know how much I need this!

euler's foiler

Guest

Re: need help - maclaurin series?

here is where i got the info from:

http://mathworld.wolfram.com/MaclaurinSeries.html

i tried looking at the summations too, but (2n+2)! doesn't explain the denominator, unless some simplifying is involved

and, sorry to be a real pain in the math, but what are the patterns for sin[sup]-1[/sup] and cos[sup]-1[/sup]? i don't need tan[sup]-1[/sup], its clear

thanks for the help guys, you're doing me a  big favour ^^

euler's foiler

Guest

Re: need help - maclaurin series?

Ok, I figured out it uses Bernoulli Numbers... (I hate those things)

but through simplifying I get 1/15 when I plug in n=1, not 2/15... someone help?

euler's foiler

Guest

Re: need help - maclaurin series?

Never mind, got it!