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Sequence of sum

  1. Jan 31, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the sum of [itex]5^1-5^2+5^3-5^4+...-5^{98}[/itex]

    a. (5/4)(1-5^99)
    b. (1/6)(1-5^99)
    c. (6/5)(1+5^98)
    d. (1-5^100)
    e. (5/6)(1-5^98)

    2. Relevant equations



    3. The attempt at a solution

    I feel as though this is actually a simple problem and that I'm not looking at it the right way.

    [[itex]5^1 + 5^3 + 5^5....5^{97}[/itex]] + [[itex]-5^2-5^4-5^6...-5^{98}[/itex]]
     
    Last edited: Jan 31, 2013
  2. jcsd
  3. Jan 31, 2013 #2

    jbunniii

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    Do you know how to sum ##x^n## in general? What is ##x## here?
     
  4. Jan 31, 2013 #3
    ##x## will be 5?

    [tex]\sum_{i=0}^{48} (5^{2i + 1})[/tex] + [tex]\sum_{i=0}^{49} (5^{2i})[/tex]


    Never mind, I figured it out!
     
    Last edited: Jan 31, 2013
  5. Jan 31, 2013 #4

    jbunniii

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    Actually, it looks to me like
    $$-\sum_{n=1}^{98}(-5)^n$$
     
  6. Feb 1, 2013 #5
    I used Sn = [itex]\frac{a_1*(1-r^n)}{1-r}[/itex]

    Sn = [itex]\frac{5*(1-(-5)^98)}{1-(-5)}[/itex]

    = [itex]\frac{5*(1-(-5)^98)}{6}[/itex]

    = (5/6)*(1-(-5)^98)

    Thanks for your help!
     
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