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2(-1)^n = -2? Problem with (-1) to the power of natural numbers

  1. Mar 29, 2013 #1
    EDIT: Found the answer, seems I overlooked part of the solution in the learning materials ( answer extended into another page) the Solution does indeed equal what i thought it did.

    1. The problem statement, all variables and given/known data

    So this is the problem i have:

    (2(-1)^n -((n*pi)^2(-1)^n)-2)*(8/(n*pi)^3)

    where n = any natural number

    this equation equals:

    ( (n*pi)^2-4)*(8/(n*pi)^3)

    i cannot figure out how this works, if n = 1 the equation works, but if n = 2, then shouldn't the answer be:

    ( -(n*pi)^2)*(8/(n*pi)^3)

    ?

    for simplification, removing the (8/(n*pi)^3)

    (2(-1)^n -((n*pi)^2(-1)^n)-2)

    where n = any natural number

    =

    ( (n*pi)^2-4)

    or

    ( -(n*pi)^2)

    ?


    Any help would be appreciated.


    2. Relevant equations



    3. The attempt at a solution

    See above.
     
    Last edited: Mar 29, 2013
  2. jcsd
  3. Mar 29, 2013 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If n is even then (-1)^n= 1. If n is odd, (-1)^n= -1. So
    1) if n is even, 2(-1)^n -((n*pi)^2(-1)^n)-2)= 2- (n^2 pi^2- 2)= 4- n^2 pi^2

    2) if n is odd, 2(-1)^n -((n*pi)^2(-1)^n)-2)= -2-(-n^2 pi^2- 2)= n^2 pi^2
     
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