Originally Posted by **Natasha1**

I can't do this one :-(

Prove from the definition that $\displaystyle a_n=\frac{n^2 + 3n}{n^2 +2} $ -> 1 as n -> $\displaystyle \infty$

My lecturer wrote on the board that we should be answering the question as follows (he never gave us an example though!):

For a given positive h you must ensure that the difference of and 1 can be made to stay less than h. When you have an expression for the difference, look for a related simpler expression that can easily be made less than h.

Haven't got a clue, please help.