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Homework Help: Complicated Function

  1. Jun 1, 2010 #1
    Hi,
    please find attached the problem and the answer. I can't anderstand the first and second step of the answer. I only need a link for the topic or maybe method the used. Bdw I haven't tried to figure out the second answer but for now I only need help tackling the first one.
     

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  2. jcsd
  3. Jun 1, 2010 #2

    Mark44

    Staff: Mentor

    There is no attachment...
     
  4. Jun 1, 2010 #3
    thanks for telling.. I uploaded it now :)
     
  5. Jun 1, 2010 #4

    HallsofIvy

    User Avatar
    Science Advisor

    I have the feeling I have done this before!

    You have the equation [itex]f(n)= 15^n+ 8^{n-2}[/itex] and want to write f(n+1)- 8 f(n) as a multiple of [itex]15^n[/itex].

    Okay, [itex]f(n+1)= 15^{n+1}+ 8^{n+1- 2}[/itex][itex]= 15^{n+1}- 8^{n-1}[/itex] and [itex] 8f(n)= 8(15^n)- 8^{n-2})=[/itex][itex] 8(15^n)- 8(8^{n-2})= [/itex][itex]8(15^n)- 8^{n-1}[/itex]

    Now, when you subtract the two "[itex]8^{n-1}[/itex]" terms cancel and you get [itex]15^{n+1}- 8(15^n)= 15(15^n)- 8(15^n)= (15- 8)15^{n+1}[/itex].
     
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