Divergent and Convergent

**nerdo** · October 25th 2009, 06:43 AM

Can someone please help me with the following question:

Thanks

Nerdo

**utopiaNow** · October 25th 2009, 08:14 AM

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.

**nerdo** · October 25th 2009, 08:15 AM

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

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