Whats the difference between diverge and converge???

- anonymous

Whats the difference between diverge and converge???

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- hba

go to the physics portion

- TuringTest

what? no it's a math Q

- anonymous

but its in algebra 2

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## More answers

- hba

k sorry

- anonymous

Diverge means separate, converge means meet.

- TuringTest

converge is to "settle down" on a finite falue

- TuringTest

value*

- TuringTest

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

- hba

@pratu043 it is maths not physics

- anonymous

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

- anonymous

Does it go to infinity?

- anonymous

Or does it go to a specific value?

- TuringTest

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

- anonymous

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."

- anonymous

it goes infinitly

- anonymous

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

- TuringTest

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

- anonymous

If it went to infinity then the sequence will increase exponentially

- anonymous

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

- anonymous

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.

- TuringTest

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

- anonymous

no all that it gave me was what i put up

- TuringTest

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

- TuringTest

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

- TuringTest

identify |r| *

- anonymous

is it 1/5?

- anonymous

Yes, r=1/5

- anonymous

so it converges and it has a sum right?

- anonymous

Yes

- anonymous

Thanks!

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