sambellamy
Junior Member
- Joined
- Oct 21, 2014
- Messages
- 53
I have to determine for which positive integers k the series will be convergent:
Ʃn=1∞ (n!)2 / (kn)!
I know that k=1 will cause the values to grow without bound and diverge. I also have determined that k = 2 oranything greater will cause the denominator to grow more than the numerator and the values will converge on zero. I am not sure how to approach this mathematically to show that it is ture. I tried with the ratio test and the example that k = 2, but none of the terms I got could cancel another out. What does (kn)! break down into? I know that k(n!) and kn(n!) are too small compared to (kn)!, and so is k!n!. Please help!
Ʃn=1∞ (n!)2 / (kn)!
I know that k=1 will cause the values to grow without bound and diverge. I also have determined that k = 2 oranything greater will cause the denominator to grow more than the numerator and the values will converge on zero. I am not sure how to approach this mathematically to show that it is ture. I tried with the ratio test and the example that k = 2, but none of the terms I got could cancel another out. What does (kn)! break down into? I know that k(n!) and kn(n!) are too small compared to (kn)!, and so is k!n!. Please help!