# The hardest ever

The hardest ever,,,

## Homework Statement

40) for which positive intigers k is the following sries convergent:
(n!) ^2 / (kn)!

## Homework Equations

using the ratio test the limit should be less than 1

## The Attempt at a Solution

I tried the ratio test, but I got inifinty?

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tiny-tim
Homework Helper
Hi remaan!
for which positive intigers k is the following sries convergent:
(n!) ^2 / (kn)!

using the ratio test the limit should be less than 1

I tried the ratio test, but I got inifinty?
Hint: which is larger, (5!)2 or 10! ?

Hurkyl
Staff Emeritus
Gold Member

using the ratio test the limit should be less than 1
No -- it could be less than 1, but it doesn't have to. You're making some assumptions when you said that; what are they? (Or, I suppose you could have just made a mistake)

I tried the ratio test, but I got inifinty?
What does that tell you?

Hi remaan!

Hint: which is larger, (5!)2 or 10! ?
Hi,

mm, 1o! is greater, but how can I benifit from this in finding K ??

No -- it could be less than 1, but it doesn't have to. You're making some assumptions when you said that; what are they? (Or, I suppose you could have just made a mistake)

I mention that because the question says "positive intergers,"

What does that tell you?
It tells that the series is not alternating and I can't ( ratio test ) to find the k .

Hurkyl
Staff Emeritus