1. ## Proof of convergence

Prove from the definition that the sequences of the form

(An + B)/(Cn^2 + D)

where A,B,C,D 2 R,C > 0,D 0
are all convergent.

Don't really know where to go with this...my teacher didn't explain how to prove convergence well, so I'm pretty stuck
All I have is that I should prove by showing there exists a G st. for all epsilon > 0 there is an N > 0 st. for all n>N |(An+B)/(Cn^2+D) -G| < epsilon

2. Originally Posted by mistykz
Prove from the definition that the sequences of the form

(An + B)/(Cn^2 + D)

where A,B,C,D 2 R,C > 0,D 0
are all convergent.

Don't really know where to go with this...my teacher didn't explain how to prove convergence well, so I'm pretty stuck
All I have is that I should prove by showing there exists a G st. for all epsilon > 0 there is an N > 0 st. for all n>N |(An+B)/(Cn^2+D) -G| < epsilon
Since all the coefficients are all positive we see that $\displaystyle \left|\frac{An+B}{Cn^2+D}\right|=\frac{An+B}{Cn^2+ D}\leqslant\frac{An}{Cn^2}=\frac{A}{C}\frac{1}{n}$. Thus,for any $\displaystyle \varepsilon>0$ we can make $\displaystyle \left|\frac{An+B}{Cn^2+D}\right|<\varepsilon$ by choosing $\displaystyle n>\frac{1}{\frac{A}{C}\varepsilon}$

3. That makes sense...but I think I typo'd this:
where A,B,C,D 2 R,C > 0,D 0