## petegutz 3 years ago Whats the difference between diverge and converge???

1. hba

go to the physics portion

2. TuringTest

what? no it's a math Q

3. petegutz

but its in algebra 2

4. hba

k sorry

5. pratu043

Diverge means separate, converge means meet.

6. TuringTest

converge is to "settle down" on a finite falue

7. TuringTest

value*

8. TuringTest

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

9. hba

@pratu043 it is maths not physics

10. petegutz

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

11. Monkeyball

Does it go to infinity?

12. Monkeyball

Or does it go to a specific value?

13. TuringTest

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

14. nbouscal

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."

15. petegutz

it goes infinitly

16. Monkeyball

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

17. TuringTest

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

18. Monkeyball

If it went to infinity then the sequence will increase exponentially

19. nbouscal

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

20. nbouscal

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.

21. TuringTest

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

22. petegutz

no all that it gave me was what i put up

23. 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?

24. TuringTest

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

25. TuringTest

identify |r| *

26. petegutz

is it 1/5?

27. nbouscal

Yes, r=1/5

28. petegutz

so it converges and it has a sum right?

29. nbouscal

Yes

30. petegutz

Thanks!