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-   -   General Term for Cos X in Maclaurin Series (https://www.askmehelpdesk.com/showthread.php?t=339638)

  • Apr 9, 2009, 04:26 PM
    johnmurray100
    General Term for Cos X in Maclaurin Series
    The 1st term of the maclaurin series for Cos x is 1.
    The Genreral Term is {(-1)^n}*{x(2*n)}/{(2*n)!}.

    This will yield 1st term =1 only if n=0

    I would expect Term 1 to be generated by setting n=1 not 0

    Can you explain where my reasoning is wrong please
  • Apr 9, 2009, 04:57 PM
    galactus



    The first term is 1 because a 0 exponent yields 1 as well as 0! If you subbed in n=1, you would get

    . Just as the second term yields.
  • Apr 10, 2009, 03:04 AM
    johnmurray100
    Hello Galactus
    Thank very much for your reply.
    The problem I have is that a similar expansion for the Sin Series requires setting n=1 to get the first term.
    I am at a loss to know why n=0 for 1st term of Cos X series & n=1 for 1st term of Sin Series.

    I would expect n=1 to yield 1st term of both Series.

    The general term for Sin Series is {(-1)^(n+!)}*{(x)^(2*n-1)}/{(2*n-1)!}

    Setting N=0 yields -1! In denominator.

    I would appreciate any guidance on this please
  • Apr 10, 2009, 09:01 AM
    galactus
    Look at the series. It is rather obvious what you get when you plug in 0 or 1.



    Now, plug in n=0:



    Plug in n=1:



    See now?

    Those are the first two terms of the expansion.




    Let's look at the series for e:



    Plug in n=0:



    Plug in n=1:



    And so on and so forth
  • Apr 10, 2009, 02:48 PM
    johnmurray100

    Hello galactus,
    Thank you for reply.

    The denominator you have used is (2*n+1)!

    The denominator that I have is (2*n-1)!
    Have I got the wrong denominator?
  • Apr 10, 2009, 03:26 PM
    galactus
    For the sine series? You have the wrong one. It is (2n+1)!

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