Convergence Test for Series with Square Root Terms

[lha08]

Homework Statement

Using Comparison test and LCT, determine whether it is convergent or divergent:

(summation n=1 to infinity) sqrt(n+2)/(2n^2+n+1)

Homework Equations

The Attempt at a Solution

i compared it with sqrt(x)/2n^2 which is 1/2n^(3/2)
and then the answer showed something weird...they had to plug in a number (e.g. 1) which reversed the inequality sign... to sqrt(n+2)/(2n^2+n+1) is larger than 1/2n^(3/2)...does anyone know why?

 

[Dick]

Then pick a different comparison. You want to make the numerator larger and the denominator smaller if you think it converges. Be creative! How about comparing with sqrt(n+n)/(2n^2)?