Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Error terms in Taylor Series

  1. Dec 16, 2008 #1
    It is known that
    [tex] \sum\limits_{k = 0}^\infty {\frac{{N^k }}{{k!}}} = e^N[/tex]

    I am looking for any asymptotic approximation which gives

    [tex] \sum\limits_{k = 0}^M {\frac{{N^k }}{{k!}}} = ? [/tex]
    where [tex]M\leq N[/tex] an integer.

    This is not an homework
  2. jcsd
  3. Dec 16, 2008 #2
    I'm only being a little facetious if I point out that the sum is asymptotically equal to e^N.

    Want more accuracy? It's better approximated by e^N-[x^(N+1)]/(N+1)!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Error terms in Taylor Series
  1. Taylor Algebra? (Replies: 0)

  2. Taylor series (Replies: 2)

  3. Nth term (Replies: 1)