# What are two examples of convergent sequences?

##### 1 Answer

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#### Explanation:

Any constant sequence is convergent. For any

#lim_(n->oo)1 = 1# #lim_(n->oo)pi^e = pi^e#

Any sequence in which the numerator is bounded and the denominator tends to

#lim_(n->oo)1/n = 0# #lim_(n->oo)(100sin(n))/ln(n) = 0#

If

#lim_(n->oo)(1/2)^n = 0# #lim_(n->oo)(k/(k+1))^n = 0# for#k in [0, oo)#

If

and

then

#lim_(n->oo)(2n+1)/(n+5) = 2/1 = 2# #lim_(n->oo)(4n^7-2n^2+1)/(-10n^7+10n^6+1000) = 4/(-10) = -2/5#

#n^n# #n!# #C^n, |C| > 1# #n^C# #log(n)#

A term higher on the list divided by a term lower on the list will tend to

#lim_(n->oo) (n!)/n^n = 0# #lim_(n->oo) (2log(n) + n^2 + e^n)/(n!) = 0#

If

This is actually the geometric series formula.

In some places, this is how

There are many different ways to make convergent sequences. Some are intuitive. Some are not. Most require more justification than is provided here if the question is to show why they converge, but it is still useful to know what sorts of sequences converge and how.

And, finishing with a doozy, we have the Gaussian integral: