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hal_stirrup

  • 2 years ago

In Infinite series the sum of infinite series is the (partial sum). Is that because its infinite and we can't sum up an infinite series ??

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  1. hal_stirrup
    • 2 years ago
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    thanks of viewing.

  2. estudier
    • 2 years ago
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    Well, it's convenient for looking at convergence and limits, no?

  3. hal_stirrup
    • 2 years ago
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    yes. it is.

  4. hal_stirrup
    • 2 years ago
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    so what do you think of my question?.

  5. estudier
    • 2 years ago
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    Well, we can sum up the series (if the limit of partial sums exists)

  6. hal_stirrup
    • 2 years ago
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    we can? how do we know if the limit of partial sums exists?

  7. estudier
    • 2 years ago
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    Convergence

  8. hal_stirrup
    • 2 years ago
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    so your saying if a series Converges it partial sums exists

  9. estudier
    • 2 years ago
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    Well, if a series diverges, there wouldn't be any convergence, right?

  10. hal_stirrup
    • 2 years ago
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    yes

  11. estudier
    • 2 years ago
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    And you wouldn't be able to add it up however hard you tried

  12. hal_stirrup
    • 2 years ago
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    yes BUT because its a infinite series whether it converges or diverges we cant sum it all up?

  13. estudier
    • 2 years ago
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    That's what I'm saying, if it converges then you can (usually) add it up (analytically).

  14. hal_stirrup
    • 2 years ago
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    i see what your saying sure. i just don't see the idea of converges or diverges has anything to do with the fact that a series Converges and there for the partial sums exists

  15. estudier
    • 2 years ago
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    If the series converges then you can take a limit

  16. hal_stirrup
    • 2 years ago
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    All well and good that you are saying the facts. :) i really want to understand why we can take a limit when series converges and not diverges.

  17. hal_stirrup
    • 2 years ago
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    am sorry am being a pain.

  18. estudier
    • 2 years ago
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    the limit of a divergent series is infinite and some other limits might not exist (there are shades of convergence, absolute, conditional...)

  19. estudier
    • 2 years ago
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    You must have a way, analyytically, to approach a limit (even if you do not actually ever reach it)

  20. estudier
    • 2 years ago
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    I am assuming you have studied calculus, the limit concept there is similar.

  21. hal_stirrup
    • 2 years ago
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    i see . if we say that x-----> 2 x approaches 2 . what comment would you have?

  22. hal_stirrup
    • 2 years ago
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    i have studied CAL but in a very mechanical way!

  23. estudier
    • 2 years ago
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    You can say it and it implies that the limit is 2 but doesn't say anything about how you got that.

  24. hal_stirrup
    • 2 years ago
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    do we care how we get there . is that important for us?

  25. estudier
    • 2 years ago
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    How do we know that your limit is valid?

  26. estudier
    • 2 years ago
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    The limit of 1 + 1/2 +1/4 + 1/8 ......+1/2^n has a limit of 2 Do you believe me?

  27. hal_stirrup
    • 2 years ago
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    well you told me thats

  28. estudier
    • 2 years ago
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    Ok, it's not 2 it's 3

  29. hal_stirrup
    • 2 years ago
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    no its not !

  30. estudier
    • 2 years ago
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    Anyway, the point is that it converges and it is fairly easy to establish that 2 is an upper bound and with a little more work that the sum is actually 2

  31. estudier
    • 2 years ago
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    And now I am off to bed, I'm afraid.....

  32. hal_stirrup
    • 2 years ago
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    visually . |dw:1348445954284:dw|

  33. hal_stirrup
    • 2 years ago
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    thanks you Rock. :)

  34. estudier
    • 2 years ago
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    G'night:)

  35. hal_stirrup
    • 2 years ago
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    you too

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