hal_stirrup
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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hal_stirrup
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thanks of viewing.
estudier
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Well, it's convenient for looking at convergence and limits, no?
hal_stirrup
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yes. it is.
hal_stirrup
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so what do you think of my question?.
estudier
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Well, we can sum up the series (if the limit of partial sums exists)
hal_stirrup
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we can? how do we know if the limit of partial sums exists?
estudier
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Convergence
hal_stirrup
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so your saying if a series Converges it partial sums exists
estudier
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Well, if a series diverges, there wouldn't be any convergence, right?
hal_stirrup
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yes
estudier
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And you wouldn't be able to add it up however hard you tried
hal_stirrup
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yes BUT because its a infinite series whether it converges or diverges we cant sum it all up?
estudier
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That's what I'm saying, if it converges then you can (usually) add it up (analytically).
hal_stirrup
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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
estudier
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If the series converges then you can take a limit
hal_stirrup
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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.
hal_stirrup
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am sorry am being a pain.
estudier
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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...)
estudier
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You must have a way, analyytically, to approach a limit (even if you do not actually ever reach it)
estudier
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I am assuming you have studied calculus, the limit concept there is similar.
hal_stirrup
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i see . if we say that x-----> 2 x approaches 2 . what comment would you have?
hal_stirrup
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i have studied CAL but in a very mechanical way!
estudier
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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.
hal_stirrup
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do we care how we get there . is that important for us?
estudier
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How do we know that your limit is valid?
estudier
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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?
hal_stirrup
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well you told me thats
estudier
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Ok, it's not 2 it's 3
hal_stirrup
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no its not !
estudier
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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
estudier
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And now I am off to bed, I'm afraid.....
hal_stirrup
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visually . |dw:1348445954284:dw|
hal_stirrup
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thanks you Rock. :)
estudier
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G'night:)
hal_stirrup
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you too