Question

Whats the difference between diverge and converge???

Answer 1

go to the physics portion

Answer 2

what? no it's a math Q

Answer 3

but its in algebra 2

Answer 4

k sorry

Answer 5

Diverge means separate, converge means meet.

Answer 6

converge is to "settle down" on a finite falue

Answer 7

value*

Answer 8

oh jeez, an algebra2 definition of "diverge" ?
I kind of would like to know the context

Answer 9

@pratu043 it is maths not physics

Answer 10

heres what the question is 1/5+1/25+1/125+1/625... Does the infinite geometric series converge or diverge?explain

Answer 11

Does it go to infinity?

Answer 12

Or does it go to a specific value?

Answer 13

or does it settle on no value at all and oscillate forever?

Answer 14

Algebra 2 is an interesting time to learn about this. You should at least see the formal definition, so here's that (in my words): A sequence \(a_n\) converges to a limit \(L\) iff for any given \(\epsilon\), there exists an \(N\) such that \(n>N\implies |a_n-L|<\epsilon\). That's the formal one. In english, that means, as you go on to infinity, the sequence gets as close as you like to a given value. Basically, like others have said, the sequence "settles down" to a value. Diverges simply means "does not converge."

Answer 15

it goes infinitly

Answer 16

no it does not.....the reason being that the denominator is getting bigger which means that the overall number is getting smaller.

Answer 17

@nbouscal I wish they taught me that in algebra2, but I don't think so...

Answer 18

If it went to infinity then the sequence will increase exponentially

Answer 19

Oh no, I'm sure they don't. They would never do something crazy like teach real mathematics to secondary school students :P

Answer 20

Not saying I know pedagogy better than they do, but couldn't they at least flash it on the board? One slide of a powerpoint? No? *sigh* oh well.

Answer 21

exactly^
@petegutz do you have a specific formula to use? there are a few...

Answer 22

no all that it gave me was what i put up

Answer 23

\[\sum_{n=1}^\infty ar^{n-1}=\sum_{n=0}^\infty ar^n=\frac a{1-r}\]is maybe a formula you can use?

Answer 24

the above is only true for \(|r|<1\), otherwise the series diverges
so you must identify }r| in your series

Answer 25

identify |r| *

Answer 26

is it 1/5?

Answer 27

Yes, r=1/5

Answer 28

so it converges and it has a sum right?

Answer 29

Yes

Answer 30

Thanks!