Plz help me ...for convergence/divergence?

Question

terenzreignz · Answer

Of sequences?
Series?
Integrals?

anonymous · Answer

Do you want to know an explanation/ definition?

anonymous · Answer

sequences And explanation

anonymous · Answer

If a sequence converges, each term will add up to a certain number. In the case of divergence, it will never reach a definite value.

anonymous · Answer

For example: (1/x)+(1/x^2)+(1/x^3)+..... will always diverge. Which means, it will never add up to a number, there is no sum, and it therefor, diverges.

terenzreignz · Answer

@ShaeCalc 
Stick to sequences for now...   no reason to complicate things more than necessary yet...

@Zia.ucsi you DO mean sequences, right? and not Series?  those two are related but not the same...

anonymous · Answer

Wait, don't sequences not have anything to do with divergence?

terenzreignz · Answer

A sequence is convergent if it has a limit as n goes to infinity, that is all :)
A series is convergent if the sequence of partial sums is convergent.

anonymous · Answer

oh man, I keep confusing sequences with series. Thanks for the correction. My bad :S

terenzreignz · Answer

And of course, on the other hand, a sequence is divergent if there is no limit as n goes to infinity.

terenzreignz · Answer

Okay, @Zia.ucsi 
A sequence is just a function whose domain is the set of positive integers.

In English?
It's a set of numbers in a determined order.
For example, the simple sequence $\large a_n = n$
It's simply the set of all natural numbers $$1,2,3,4,...$$

terenzreignz · Answer

So, quick quiz... name the first four terms of this sequence
$$\huge a_n=2^n$$

anonymous · Answer

thank u bro/sis

terenzreignz · Answer

Terence.... stick to Terence :)