How do I solve the inequation \sqrt{n} < \sqrt{n-1} + .01?

[Brunno]

Homework Statement

Somebody can help me with thi following problem:

\sqrt{n} - \sqrt{n-1} < 0,01

Answer: n=2501

Homework Equations

The Attempt at a Solution

 

[theJorge551]

We can't help you unless you give us some sort of indication that you've actually tried it.

 

[Brunno]

I tried this:

A=n^1/2

B= n-1)^1/2

Then i squared both terms :

[n^1/2 - (n-1)^1/2]² <0,0001

But i couldn't find the answer anyways.Just didn't work this way to me.

 

[Mark44]

For one thing, your answer is NOT going to be an equation. Instead, it will be an inequality.

To make things easier on yourself, rewrite your inequality with one of the radicals moved to the other side.
\sqrt{n} &lt; \sqrt{n-1} + .01
Now square both sides. Since you're multiplying each side by a positive number, the direction of the inequality won't change.

When you square both sides, you will end up with another radical. Just move all of the other terms to the other side so that the radical is all by itself on one side, then square both sides again.