What is a convergent sequence?

[ctg81]

Could anyone please explain "convergent sequence" with example.

 

[n.karthick]

Consider this
n+1=n/2+1/n and start from n=1. Find n+1 continuously from this relation and you will find that this sequence converges to sqrt(2)

Also the sequence
$${u_n}=\frac{3n^2-1}{n^2-5n}$$

converges to 3.

One can find many convergent sequences like this.