Attachment 25964

can anyone explain how why (kn!) / (kn+k)! is K^K in the final part of the answer?

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- November 27th 2012, 06:16 PMbakinbacon(kn)! / (kn+k)! = k^k?
Attachment 25964

can anyone explain how why (kn!) / (kn+k)! is K^K in the final part of the answer? - November 27th 2012, 06:37 PMBeanRe: (kn)! / (kn+k)! = k^k?
Oops. Didn't realize it was a limit at first glance.

- November 27th 2012, 06:52 PMbakinbaconRe: (kn)! / (kn+k)! = k^k?
i just don't know how to write out (kn+k)!.. she hardly taught us how to do factorials

- November 27th 2012, 07:23 PMBeanRe: (kn)! / (kn+k)! = k^k?
In the final part of the ratio test, divide the numerator and the denominator by n and take n to infinity which takes all of the constants to zero. The bottom simplifies to k*k for k times. The numerator simplifies to 1^(k) or 1.

- November 27th 2012, 07:28 PMBeanRe: (kn)! / (kn+k)! = k^k?
as n goes to infinity.

- November 27th 2012, 07:35 PMMarkFLRe: (kn)! / (kn+k)! = k^k?
Within the absolute value bars, disregarding the what you have are th degree polynomials in the numerator and denominator in , so we know the limit as is the ratio of the leading coefficients, which is:

And so the limit of the entire expression is: