It seems like it's impossible to get the maclaurin series of sinx, cosx, and ln(x+1) to have a series index beginning at n=0. I'm confused because I think I was taught that taylor series supposedly start at n=0. ?

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- Apr 29th 2009, 09:59 AMKaitosanMaclaurin series question
It seems like it's impossible to get the maclaurin series of sinx, cosx, and ln(x+1) to have a series index beginning at n=0. I'm confused because I think I was taught that taylor series supposedly start at n=0. ?

- Apr 29th 2009, 11:28 AMJameson
I don't quite understand your confusion. By series index, do you mean the beginning value of the sum. Like for you mean the n=0 part? Please explain your confusion a little more.

Taylor series do always start with n=0 if my above assumption is true. Note that by the formula for generating every term in a Taylor series that when you apply the fact that 0!=1 and that (the 0th derivative of f(x) is f(x)) then you are simply left with f(a), which can be 0 for a lot of things. - Apr 29th 2009, 11:45 AMKaitosan
Will you please show me the maclaurin series of cosx, sinx, and ln(x+1) with "n" beginning at zero? I can't find it...

- Apr 29th 2009, 11:55 AMrunning-gag
The maclaurin series of f is

For , and

Therefore the maclaurin series of cos x is - Apr 29th 2009, 12:05 PMJester
- Apr 29th 2009, 12:06 PMKaitosan
Thanks guys, I was just confused about few things.