# Homework Help: A quick Limit

1. Nov 24, 2007

### Mattofix

1. The problem statement, all variables and given/known data

Does xn converge (Sum from n=1 to infinity) of xn = 1/(n + SQRTn)

2. Relevant equations

Using comparision test

3. The attempt at a solution

I separted into fractions of 1/SQRTn - 1/(1 + SQRTn) and i know that both of these diverge since the power of n is less than one but am stuck as to whether is converges or diverges and how to prove it...

2. Nov 24, 2007

### Kummer

$$\frac{1}{n+n}\leq \frac{1}{n+\sqrt{n}}$$

3. Nov 24, 2007

### Mattofix

therefore xn divereges...?

4. Nov 24, 2007

### sutupidmath

yeah that is right, since the harmonic series diverges, it also diverges when we multiply it by a constant.

5. Nov 24, 2007

### Kummer

Non-zero constant.

Not to offend you but that is what I like to call a "physics-type mistake".

6. Nov 24, 2007

### sutupidmath

yeah that is what i actually meant, but thnx for pointing it out. and not am not offended in any way.