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5^(n+1) - 1 = 4*5^n + 5^n -1 ?

  1. Sep 21, 2004 #1
    5^(n+1) - 1 = 4*5^n + 5^n -1 ??

    This is what my book says but it does not show the math in between the steps so i can't seem to grasp it. Anyone want to show me how they are equal?
  2. jcsd
  3. Sep 21, 2004 #2
    You got to look at the law of exponents: [tex] X^a*X^b=X^{a+b}.[/tex] This comes about because, say X^4*X^2=(XXXX)(XX)=X^6.

    See: http://www.gomath.com/htdocs/lesson/exponent_lesson1.htm [Broken]
    Last edited by a moderator: May 1, 2017
  4. Sep 22, 2004 #3
    I understand that part but where does the four come from?
  5. Sep 22, 2004 #4
    The 4 seems arbitrary to me but it works as long as you have the 1 coefficient of the other 5^n term. Here's what I mean

    5^(n+1) = 5*5^n yes?
    This also equals

    4*5^n + 1*5^n

    or 3*5^n + 2*5^n

    It's not there for any reason other than to confuzzle you from what I see.
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