anonymous
  • anonymous
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 ??
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
thanks of viewing.
anonymous
  • anonymous
Well, it's convenient for looking at convergence and limits, no?
anonymous
  • anonymous
yes. it is.

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anonymous
  • anonymous
so what do you think of my question?.
anonymous
  • anonymous
Well, we can sum up the series (if the limit of partial sums exists)
anonymous
  • anonymous
we can? how do we know if the limit of partial sums exists?
anonymous
  • anonymous
Convergence
anonymous
  • anonymous
so your saying if a series Converges it partial sums exists
anonymous
  • anonymous
Well, if a series diverges, there wouldn't be any convergence, right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
And you wouldn't be able to add it up however hard you tried
anonymous
  • anonymous
yes BUT because its a infinite series whether it converges or diverges we cant sum it all up?
anonymous
  • anonymous
That's what I'm saying, if it converges then you can (usually) add it up (analytically).
anonymous
  • anonymous
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
anonymous
  • anonymous
If the series converges then you can take a limit
anonymous
  • anonymous
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.
anonymous
  • anonymous
am sorry am being a pain.
anonymous
  • anonymous
the limit of a divergent series is infinite and some other limits might not exist (there are shades of convergence, absolute, conditional...)
anonymous
  • anonymous
You must have a way, analyytically, to approach a limit (even if you do not actually ever reach it)
anonymous
  • anonymous
I am assuming you have studied calculus, the limit concept there is similar.
anonymous
  • anonymous
i see . if we say that x-----> 2 x approaches 2 . what comment would you have?
anonymous
  • anonymous
i have studied CAL but in a very mechanical way!
anonymous
  • anonymous
You can say it and it implies that the limit is 2 but doesn't say anything about how you got that.
anonymous
  • anonymous
do we care how we get there . is that important for us?
anonymous
  • anonymous
How do we know that your limit is valid?
anonymous
  • anonymous
The limit of 1 + 1/2 +1/4 + 1/8 ......+1/2^n has a limit of 2 Do you believe me?
anonymous
  • anonymous
well you told me thats
anonymous
  • anonymous
Ok, it's not 2 it's 3
anonymous
  • anonymous
no its not !
anonymous
  • anonymous
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
anonymous
  • anonymous
And now I am off to bed, I'm afraid.....
anonymous
  • anonymous
visually . |dw:1348445954284:dw|
anonymous
  • anonymous
thanks you Rock. :)
anonymous
  • anonymous
G'night:)
anonymous
  • anonymous
you too

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