# Convergence of sequence

• Sep 21st 2009, 08:52 PM
roshanhero
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?
• Sep 21st 2009, 09:12 PM
redsoxfan325
Quote:

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 $n>N$,

$\left|\left(\frac{1}{n}+1\right)-1\right|=\left|\frac{1}{n}\right|<\left|\frac{1}{1/\epsilon}\right|=\epsilon$
• Sep 23rd 2009, 12:20 AM
roshanhero
How do we pick N=1/epsilon
• Sep 23rd 2009, 06:33 AM
HallsofIvy
Do you understand what "pick" means?? You just say "if $N> 1/\epsilon$ then ..."