# Thread: Let alpha be a real number, alpha > -1 now show that

1. ## Let alpha be a real number, alpha > -1 now show that

lim n approachs infinity. the intergral from 1 to N (x^-1) dx / the intergral from 1 to N (x^alpha)dx = 0

use the tergral from 1 to n= intergral from 1 to k + intergral form k to n

2. ## Re: Let alpha be a real number, alpha > -1 now show that

Originally Posted by sbacon1991
lim n approachs infinity. the intergral from 1 to N (x^-1) dx / the intergral from 1 to N (x^alpha)dx = 0

use the tergral from 1 to n= intergral from 1 to k + intergral form k to n

$\lim_{n\to\infty}\frac{\int_1^n \frac{1}{x}dx}{\int_1^n x^{\alpha}dx}=\lim_{n\to\infty} \frac{\ln{n}}{\frac{n^{\alpha+1}}{\alpha+1}-\frac{1}{\alpha+1}}=...$

3. ## Re: Let alpha be a real number, alpha > -1 now show that

using the de nition of the Riemann integral can you prove it for?

4. ## Re: Let alpha be a real number, alpha > -1 now show that

Originally Posted by sbacon1991
using the de nition of the Riemann integral can you prove it for?
Introducing a Riemann sum into this problem would complicate it beyond all reason. It calls for a simple application of l'Hopital's rule.

5. ## Re: Let alpha be a real number, alpha > -1 now show that

is there any more info which can be given for the question?

6. ## Re: Let alpha be a real number, alpha > -1 now show that

Originally Posted by sbacon1991
is there any more info which can be given for the question?
Do you know any basic calculus?
If not, this is a waste of time going forward.

yes i do