# Math Help - Help with Quantifiers

1. ## Help with Quantifiers

Can someone help me? I'm stuck with this:

Prove or give a counterexample to the following statement: For each positive integer a, there exists a positive integer b such that

I'd appreciate any help.

2. ## Re: Help with Quantifiers

$\frac{1}{2b^2+b}<\frac{1}{ab^2}$ iff $2b^2+b>ab^2$. In the latter inequality, both sides are quadratic polynomials in b. I understand that this problem is formally about quantifiers, but essentially it is about comparing two quadratic functions. For this reason, if you need help with this, it would make sense to post the problem to pre-university Algebra or Pre-calculus subforums.

3. ## Re: Help with Quantifiers

Originally Posted by JoannaEris
Prove or give a counterexample to the following statement: For each positive integer a, there exists a positive integer b such that
Is there a solution if $a=3~?$