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petegutz

Whats the difference between diverge and converge???

  • one year ago
  • one year ago

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  1. hba
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    go to the physics portion

    • one year ago
  2. TuringTest
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    what? no it's a math Q

    • one year ago
  3. petegutz
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    but its in algebra 2

    • one year ago
  4. hba
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    k sorry

    • one year ago
  5. pratu043
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    Diverge means separate, converge means meet.

    • one year ago
  6. TuringTest
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    converge is to "settle down" on a finite falue

    • one year ago
  7. TuringTest
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    value*

    • one year ago
  8. TuringTest
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    oh jeez, an algebra2 definition of "diverge" ? I kind of would like to know the context

    • one year ago
  9. hba
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    @pratu043 it is maths not physics

    • one year ago
  10. petegutz
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    heres what the question is 1/5+1/25+1/125+1/625... Does the infinite geometric series converge or diverge?explain

    • one year ago
  11. Monkeyball
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    Does it go to infinity?

    • one year ago
  12. Monkeyball
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    Or does it go to a specific value?

    • one year ago
  13. TuringTest
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    or does it settle on no value at all and oscillate forever?

    • one year ago
  14. nbouscal
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    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."

    • one year ago
  15. petegutz
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    it goes infinitly

    • one year ago
  16. Monkeyball
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    no it does not.....the reason being that the denominator is getting bigger which means that the overall number is getting smaller.

    • one year ago
  17. TuringTest
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    @nbouscal I wish they taught me that in algebra2, but I don't think so...

    • one year ago
  18. Monkeyball
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    If it went to infinity then the sequence will increase exponentially

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

    • one year ago
  20. nbouscal
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    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.

    • one year ago
  21. TuringTest
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    exactly^ @petegutz do you have a specific formula to use? there are a few...

    • one year ago
  22. petegutz
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    no all that it gave me was what i put up

    • one year ago
  23. TuringTest
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    \[\sum_{n=1}^\infty ar^{n-1}=\sum_{n=0}^\infty ar^n=\frac a{1-r}\]is maybe a formula you can use?

    • one year ago
  24. TuringTest
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    the above is only true for \(|r|<1\), otherwise the series diverges so you must identify }r| in your series

    • one year ago
  25. TuringTest
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    identify |r| *

    • one year ago
  26. petegutz
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    is it 1/5?

    • one year ago
  27. nbouscal
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    Yes, r=1/5

    • one year ago
  28. petegutz
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    so it converges and it has a sum right?

    • one year ago
  29. nbouscal
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    Yes

    • one year ago
  30. petegutz
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    Thanks!

    • one year ago
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