Estimating ln n and Proving its Limit as n Approaches Infinity

[kimberu]

Homework Statement

using the following definition: ln x = $$\int dx/x$$, give best possible upper and lower estimates of ln n, n a positive integer.

then, use this result to show that the limit of the function as n approaches infinity is infinity.

Homework Equations

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The Attempt at a Solution

Unfortunately I have no idea what to attempt -- I don't know how to find estimates, and I'm not really sure what that means -- this is for a history of math class so I have no textbook context to look though either. Any explanations/tips would be very helpful, thanks!

 

[LCKurtz]

You probably mean to define

$$\ln{(x)} = \int_1^x\, \frac 1 t\, dt$$

Try looking at upper and lower rectangular approximating sums.