For Ratio Test...

[Perez.Julio79]

How do I simplify the following to get its limit:

k^99
-------
(k+1)^99


There is now way that I'm going to expand out the denominator. I'm sure that there is a simpler way to cancel out the numerator but I simply can't remember what the process is towards doing that. Any help would be appreciated thanks.

 

[Deleted member 4993]

How do I simplify the following to get its limit:

k^99
-------
(k+1)^99


There is now way that I'm going to expand out the denominator. I'm sure that there is a simpler way to cancel out the numerator but I simply can't remember what the process is towards doing that. Any help would be appreciated thanks.

(k+1)^99 = k^99 *(1 + 1/k)^99

 

[stapel]

How do I simplify the following to get its limit:

k^99
-------
(k+1)^99

The limit of "it" as k goes to what?

 

[pka]

How do I simplify the following to get its limit:

k^99
-------
(k+1)^99

Frankly, I do not see what this has to do with the ratio test. If you would post the exact question it would help.

That said: \(\displaystyle \dfrac{{{k^{99}}}}{{{{(k + 1)}^{99}}}} = {\left( {\dfrac{k}{{k + 1}}} \right)^{99}} = {\left( {1 - \dfrac{1}{{k + 1}}} \right)^{99}}\)