Direct Comparison Test inequality help

[dami]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

I looked at the graphs of Ln (n) vs. n^(k)

 

[Mark44]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

I looked at the graphs of Ln (n) vs. n^(k)

And what did you find out?

Also, how did you graph n^k?

 

[dami]

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

 

[Mark44]

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

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.

 

[dami]

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

 

[dami]

Just plotted the graph