Question

Can someone explain this to me? What does that mean that a series diverges or converges, and how do I determine that ?

Answer 1

no clue:)

Answer 2

no:)

Answer 3

he is probably able to help me with this.

Answer 4

probley. but mabey not. then what?

Answer 5

I'll tag someone else then. I am sure there are people who know this math well.

Answer 6

ya I guess.

Answer 7

@BangkokGarrett can you help me ?

Answer 8

@╰☆╮Openstudier╰☆╮

Answer 9

@pgpilot326 ?

Answer 10

http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx

Answer 11

still need help?

Answer 12

Yes, I still do.

Answer 13

if I write down a series and the 2nd term is bigger than the first term, the 3rd term bigger than the 2nd and so on .... like this:
1,5,9,14,.....
can you continue write down some more? just next term is bigger than its left term

Answer 14

Wait, 1,5,9,13 ? not 14 right ?

Answer 15

watever, just the concept, write some more bigger, bigger, bigger....

Answer 16

ok, 13, 17, 21 and +4 each time. nth term = a (n-1) + 4

Answer 17

good. so, do you agree with me that the term will be large, large and large forever?

Answer 18

Yes... forever if
\[\sum_{~~}^{∞}\]

Answer 19

I get the idea. And if it gets bigger and bigger that means what ?

Answer 20

ok, can you guess the term of 1000000000 th? No, right? so, the sequence is diverge

Answer 21

I can guess that term.

1+(10000000 times 4)

Answer 22

what if I give you the term of infinite point?

Answer 23

OK, if the term is n∞ then yeah... I see.
But, Diverges, means that it gets larger,

So converges is when it gets smaller and smaller?

Answer 24

12345000000000000000000000000234567000000000000th?

Answer 25

no way to calculate. :)

Answer 26

Yeah, I see it gets bigger and bigger

Answer 27

you are correct, if the term start at 1, the next one is half of the previous one: 1/2, the next is half of its previous: 1/4 ... and so on
If I take the term of 100th, so the quotient is small, if I take the term of 10000000000th, for sure I cannot know how small it is. However, all I know is it will be closed to 0, that is converge.

Answer 28

Some series converge to 2, others converge to some value, The common think is it down to some where

Answer 29

Ok, so in geom. series with r<1 the terms of series "converge" , "approaching" zero, and the sum approaches some number less than 1.

Answer 30

ot to sum more than 1, but after 5 terms the approximate sum won't change

Answer 31

YES !