## petegutz Group Title Whats the difference between diverge and converge??? 2 years ago 2 years ago

1. hba Group Title

go to the physics portion

2. TuringTest Group Title

what? no it's a math Q

3. petegutz Group Title

but its in algebra 2

4. hba Group Title

k sorry

5. pratu043 Group Title

Diverge means separate, converge means meet.

6. TuringTest Group Title

converge is to "settle down" on a finite falue

7. TuringTest Group Title

value*

8. TuringTest Group Title

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

9. hba Group Title

@pratu043 it is maths not physics

10. petegutz Group Title

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

11. Monkeyball Group Title

Does it go to infinity?

12. Monkeyball Group Title

Or does it go to a specific value?

13. TuringTest Group Title

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

14. nbouscal Group Title

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 Group Title

it goes infinitly

16. Monkeyball Group Title

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

17. TuringTest Group Title

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

18. Monkeyball Group Title

If it went to infinity then the sequence will increase exponentially

19. nbouscal Group Title

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 Group Title

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 Group Title

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

22. petegutz Group Title

no all that it gave me was what i put up

23. TuringTest Group Title

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

24. TuringTest Group Title

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

25. TuringTest Group Title

identify |r| *

26. petegutz Group Title

is it 1/5?

27. nbouscal Group Title

Yes, r=1/5

28. petegutz Group Title

so it converges and it has a sum right?

29. nbouscal Group Title

Yes

30. petegutz Group Title

Thanks!