Series (Geometric?)

  • Thread starter goraemon
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  • #1
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Homework Statement



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

Homework Equations




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.
 

Answers and Replies

  • #2
UltrafastPED
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What happens if you pull a 4 from every term - starting from n=1?
 
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  • #3
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What happens if you pull a 4 from every term - starting from n=1?
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!
 
  • #4
Ray Vickson
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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!
Well, do YOU think it is right?
 
  • #5
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Well, do YOU think it is right?
...yes? But then again, I wouldn't be here if I were always right just because I think I am.
 
  • #6
Ray Vickson
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...yes? But then again, I wouldn't be here if I were always right just because I think I am.
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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