# Homework Help: Direct Comparison Test inequality help

1. Jul 13, 2010

### dami

1. The problem statement, all variables and given/known data

Explain why the Direct Comparison Test allows us to use the inequality Ln n < n^(1/10) even though it is not true for a great many n values.

2. Relevant equations

3. The attempt at a solution
I looked at the graphs of Ln (n) vs. n^(k)

2. Jul 13, 2010

### Staff: Mentor

Re: Dct

And what did you find out?

Also, how did you graph nk?

3. Jul 13, 2010

### dami

Re: Dct

Actually, ln n < n^{1/10} is only true for n < 3 (for integer values of n).

4. Jul 13, 2010

### Staff: Mentor

Re: Dct

That is incorrect. The statement ln n < n.1 is true for n = 3, and it is also true for a lot of much larger values.

In this problem you're supposed to provide justification for the assertion that ln n < n.1 for some infinitely long interval.

5. Jul 13, 2010

### dami

Re: Dct

Thanks. Just realized I have been looking at the question the wrong way

6. Jul 13, 2010

### dami

Re: Dct

Just plotted the graph