anonymous
  • anonymous
lim n tends to infinity sum from k=0 to n (nCk)/ (n^k)(k+3) where nCk is n!/(k!(n-k)!) How do you express this sum as an integration?
Mathematics
katieb
  • katieb
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Owlfred
  • Owlfred
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anonymous
  • anonymous
\[\frac{nCk}{ n^k (k+3)}\]?
slaaibak
  • slaaibak
Anyway you can give this more visually? I'm not 100% how the question looks like

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anonymous
  • anonymous
or
anonymous
  • anonymous
\[\frac{nCk}{n^k}(k+3)\]
anonymous
  • anonymous
k+3 is in the denominator
anonymous
  • anonymous
ok
anonymous
  • anonymous
easier way is start with the expansion (1+x)^n
anonymous
  • anonymous
(1+x)^n = nC0 + nC1x + nC2 x^2 + .... nCk x^k + ... nCn x^n
slaaibak
  • slaaibak
\[\lim_{n \rightarrow \infty} \sum_{k=0}^{n} nCr (n^k)/(k+3) \] ?
anonymous
  • anonymous
(1+n)^x = xC0 + xC1 n + xC2 n^2 + .... +xCk n^k + .... x Cx n^x
anonymous
  • anonymous
n^k and k+3 are in the denominator numerator is only nCk
anonymous
  • anonymous
well I know what the solution to the integral is, do you want to know that? maybe it would help you in deciding what the integral should look like. I'm not sure myself how to write the integral yet
anonymous
  • anonymous
no i want what the integral is the answer is not really important...

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