Does xn Converge? A Comparison Test

[Mattofix]

Homework Statement

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

Homework Equations

Using comparision test

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...

 

[Kummer]

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

 

[Mattofix]

therefore xn divereges...?

 

[sutupidmath]

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

 

[Kummer]

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

Non-zero constant.

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

 

[sutupidmath]

Non-zero constant.

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

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