If it is, how would you go about doing it?

Printable View

- Apr 30th 2009, 05:08 PMleverin4Is it possible to solve this inequality for n?
If it is, how would you go about doing it?

- May 1st 2009, 08:30 AMleverin4
Lack of a response tells me no. Can anyone give me advice on approximating n?

- May 3rd 2009, 09:47 PMleverin4
I tried using Mathematica, but it couldn't do it. I don't remember the exact error message, but I'll try it again tomorrow and post it. Meanwhile, isn't there anyone that can give me some advice on how to simplify it?

- Jun 25th 2009, 12:22 AMTWiX
It is old thread , i know

but am interesting to know the answer *_* - Aug 5th 2009, 12:22 PMOpalg
It would be hard to find a necessary and sufficient condition on n for this inequality to hold. However, problems like this usually occur in a first course on analysis, and the aim there is not to find the

*smallest*value of n that will satisfy the inequality, but to find*some*number N such that all values of n gretaer than N will satisfy the inequality. In that case, you can make the problem much easier by getting a rough upper bound for the left side of the inequality.

For example, . If you can find a value of N such that whenever n>N, it will follow that the original inequality will hold whenever n>N. (Here, K stands for some given large number, such as 1000001.)

But , so take N to be any integer greater than and your inequality will hold for all n>N.

Just to emphasise, is not the smallest number with that property. If you want to find that number, you can use a computer to check all the values of N from 1 to , and it will tell you which is the first one to make the inequality true.