# What is meant by a convergent sequence?

##### 1 Answer

Jan 8, 2015

A sequence is said to be *convergent* if it's *limit* exists.

Else, it's said to be divergent.

It must be emphasized that if the limit of a sequence *divergent*.

A few examples of convergent sequences are:

#1/n# , with#lim_(n to oo) 1/n = 0# - The constant sequence
#c# , with#c in RR# and#lim_(n to oo) c = c# #(1+1/n)^n# , with#lim_(n to oo) (1+1/n)^n = e# where#e# is the base of the natural logarithms (also called*Euler's number*).

Convergent sequences play a very big role in various fields of Mathematics, from estabilishing the foundations of calculus, to solving problems in Functional Analysis, to motivating the development of Toplogy.