Sequences - monotonic or not

  1. Now I know how this works- but I came across this example and even though I know the answer- the simplification given in the explaination doesn't make sense to me.

    the squence is an= {5n/n!}
    now applying an+1 and dividing an+1/an
    the book indicates = 5/n+1

    this is what I don't get how
    (5n+1 /(n+1)!)/(5 n/n!) can simplify to that ?

    can someone explain please- what am I missing here.
    Last edited: Apr 2, 2012
  2. jcsd
  3. We have...
    [tex]\frac{5^{n+1}}{(n+1)!}\frac{n!}{5^n} = \frac{5\cdot5^{n}}{(n+1)n!}\frac{n!}{5^n}[/tex]
    ...which very easily simplifies to the expression you provided by cancelling out like terms.
  4. right - this is what is not clear to me- I am very new to pure maths
    how (n+1)! can be written as - (n+1)n!- may be I am having a dumb moment
    Last edited: Apr 2, 2012
  5. micromass

    micromass 18,536
    Staff Emeritus
    Science Advisor

    What is the definition of n! for you?
  6. well n! means = any number say 5 then multiplied by 5x4x3x2x1 ( natural numbers in hughest to lowest order)
  7. so basically product of positive integres less than or equal to n
  8. micromass

    micromass 18,536
    Staff Emeritus
    Science Advisor

    So, you have



    But then we have


    And the thing in brackets look familiar, no?? Indeed, the bracketed thing is n!

  9. thank you this makes sense- sometimes I just get frustrated with not enough explaination at beiggners level
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?
Similar discussions for: Sequences - monotonic or not