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Calculus question please help!

  1. Sep 21, 2011 #1
    1. can someone tell me what r^(n+1)*(1-r)=? I need it to solve a proof, but my math is so rusty! thanks!



    2. r^(n+1)*(1-r)
     
  2. jcsd
  3. Sep 21, 2011 #2
    What is the question...? Like the real question.
     
  4. Sep 21, 2011 #3
    prove by induction on n that
    1+r+r^2...+r^=1-r^n+1/1-r
    if r doesn't equal 1
     
  5. Sep 21, 2011 #4
    Just to be clear, you have

    [tex]r^n + \frac{1}{1 -r}[/tex] on your right hand side?
     
  6. Sep 21, 2011 #5
    oopps, sorry. it should be

    1+r+...+r^n=1-r^(n+1) / 1-r
     
  7. Sep 21, 2011 #6
    What is the base case? Let's start with that
     
  8. Sep 21, 2011 #7
    Also, shouldn't |r|<1?
     
  9. Sep 21, 2011 #8
    the what case?
     
  10. Sep 21, 2011 #9
    Base Case. You know that step you do in Induction
     
  11. Sep 21, 2011 #10
    i don't know?
     
  12. Sep 21, 2011 #11
    What can n be and cannot be?
     
  13. Sep 21, 2011 #12
    edit; mistake
     
  14. Sep 21, 2011 #13
    is it n can't be 0? but can be anything else?
     
  15. Sep 21, 2011 #14

    Dick

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    If you don't know induction, just multiply out (1+r+...+r^n)*(1-r). Many terms cancel.
     
  16. Sep 21, 2011 #15
    my textbook is saying 1-r^n+1
     
  17. Sep 21, 2011 #16
    Oh sorry I didn't see the 1 in front earlier
     
    Last edited: Sep 21, 2011
  18. Sep 21, 2011 #17

    Dick

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    Your textbook is right.
     
  19. Sep 21, 2011 #18
    try pluggin in 0
     
  20. Sep 21, 2011 #19
    n has to be greater than 0
     
  21. Sep 21, 2011 #20
    Why?
     
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