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Series (Geometric?)

  1. May 9, 2014 #1
    1. The problem statement, all variables and given/known data

    Calculate ##\sum\frac{4^{n+1}}{5^n}## (where n begins at 0 and approaches infinity).

    2. Relevant equations


    3. The attempt at a solution
    I could easily solve this if the numerator were just ##4^n## instead of ##4^{n+1}##, because then it would be a geometric series with ratio of ##\frac{4}{5}##. But I'm not sure how to approach this one. Any help would be appreciated.
     
  2. jcsd
  3. May 9, 2014 #2

    UltrafastPED

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    What happens if you pull a 4 from every term - starting from n=1?
     
  4. May 9, 2014 #3
    Oh...so the problem becomes...
    ##4*\sum(\frac{4}{5})^n=4*\frac{1}{1-\frac{4}{5}}=4*5=20##
    Is that right? Thanks!
     
  5. May 9, 2014 #4

    Ray Vickson

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    Well, do YOU think it is right?
     
  6. May 9, 2014 #5
    ...yes? But then again, I wouldn't be here if I were always right just because I think I am.
     
  7. May 9, 2014 #6

    Ray Vickson

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    What I am suggesting is that you develop some confidence in your own work. If you do things carefully, without making a mistake at any step and without violating any "rules" you are 100% guaranteed to have the correct answer. If the problem is simple enough it should be easy for you to check your own work (and that is a something you should always do, anyway); of course, for a complicated and lengthy problem the situation is different, and developing self-confidence is harder for those cases. Remember: you need to be able to do these things in an exam.

    BTW: yes, it is correct.
     
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