# Math Help - Divergent and Convergent

1. ## Divergent and Convergent

Thanks

Nerdo

2. a) Proof: Given arbitrary $\epsilon > 0$, choose $N$ such that both these inequalities hold: $N > 100$ and $N > \frac{1}{\epsilon}$. Then we know $\forall n \geq N$, $x_n = 1/n < \epsilon$. Hence $x_n \rightarrow 0$.

b) Follows pretty easily from a. you should be able to handle it.

3. Originally Posted by utopiaNow
a) Proof: Given arbitrary $\epsilon > 0$, choose $N$ such that both these inequalities hold: $N > 100$ and $N > \frac{1}{\epsilon}$. Then we know $\forall n \geq N$, $x_n = 1/n < \epsilon$. Hence $x_n \rightarrow 0$.

b) Follows pretty easily from a. you should be able to handle it.

Thanks for the help