limits of sequences using "rationalizing techniques"

[shakalandro]

I need help finding out what these "rationalizing techniques" are?

PROBLEM:

Using rationalization techniques find the limits of the following sequences
A. sqrt(n+1) - sqrt(n)
B. sqrt(n)(sqrt(n+1) - sqrt(n))

 

[galactus]

Re: limits of sequences

\(\displaystyle \left[\sqrt{n+1}-\sqrt{n}\right]_{n=1}^{\infty}\)

It converges because:

\(\displaystyle \lim_{n\to \infty}\frac{\sqrt{n+1}-\sqrt{n}}{1}\cdot\frac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n+1}+\sqrt{n}}=\lim_{n\to \infty}\frac{1}{\sqrt{n+1}+\sqrt{n}}=0\)

 

[PAULK]

Re: limits of sequences

I need help finding out what these "rationalizing techniques" are?

PROBLEM:

Using rationalization techniques find the limits of the following sequences
A. sqrt(n+1) - sqrt(n)
B. sqrt(n)(sqrt(n+1) - sqrt(n))

You learned to rationalize a denominator in high schoool. Now that you are an adult, you may apply it to other situations.

Such as:

Change sqrt(...) + sqrt(***) to a product.