# Math Help - Convergence of sequence

1. ## Convergence of sequence

Prove that the sequence {1+1/n} converges to 1 as n tends to infinity. I used the limit of {1+1/n} as n tends to infinity and got the answer,but I want to prove it by the formal definition. How can we do that?

2. Originally Posted by roshanhero
Prove that the sequence {1+1/n} converges to 1 as n tends to infinity. I used the limit of {1+1/n} as n tends to infinity and got the answer,but I want to prove it by the formal definition. How can we do that?
Pick $N=\frac{1}{\epsilon}$. Thus, for $n>N$,

$\left|\left(\frac{1}{n}+1\right)-1\right|=\left|\frac{1}{n}\right|<\left|\frac{1}{1/\epsilon}\right|=\epsilon$

3. How do we pick N=1/epsilon

4. Do you understand what "pick" means?? You just say "if $N> 1/\epsilon$ then ..."