Whats the difference between diverge and converge???

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Whats the difference between diverge and converge???

Mathematics
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  • hba
go to the physics portion
what? no it's a math Q
but its in algebra 2

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Other answers:

  • hba
k sorry
Diverge means separate, converge means meet.
converge is to "settle down" on a finite falue
value*
oh jeez, an algebra2 definition of "diverge" ? I kind of would like to know the context
  • hba
@pratu043 it is maths not physics
heres what the question is 1/5+1/25+1/125+1/625... Does the infinite geometric series converge or diverge?explain
Does it go to infinity?
Or does it go to a specific value?
or does it settle on no value at all and oscillate forever?
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."
it goes infinitly
no it does not.....the reason being that the denominator is getting bigger which means that the overall number is getting smaller.
@nbouscal I wish they taught me that in algebra2, but I don't think so...
If it went to infinity then the sequence will increase exponentially
Oh no, I'm sure they don't. They would never do something crazy like teach real mathematics to secondary school students :P
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.
exactly^ @petegutz do you have a specific formula to use? there are a few...
no all that it gave me was what i put up
\[\sum_{n=1}^\infty ar^{n-1}=\sum_{n=0}^\infty ar^n=\frac a{1-r}\]is maybe a formula you can use?
the above is only true for \(|r|<1\), otherwise the series diverges so you must identify }r| in your series
identify |r| *
is it 1/5?
Yes, r=1/5
so it converges and it has a sum right?
Yes
Thanks!

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