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hal_stirrup
 3 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 ??
hal_stirrup
 3 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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estudier
 3 years ago
Best ResponseYou've already chosen the best response.1Well, it's convenient for looking at convergence and limits, no?

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0so what do you think of my question?.

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1Well, we can sum up the series (if the limit of partial sums exists)

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0we can? how do we know if the limit of partial sums exists?

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0so your saying if a series Converges it partial sums exists

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1Well, if a series diverges, there wouldn't be any convergence, right?

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1And you wouldn't be able to add it up however hard you tried

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0yes BUT because its a infinite series whether it converges or diverges we cant sum it all up?

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1That's what I'm saying, if it converges then you can (usually) add it up (analytically).

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0i 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
 3 years ago
Best ResponseYou've already chosen the best response.1If the series converges then you can take a limit

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0All 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
 3 years ago
Best ResponseYou've already chosen the best response.0am sorry am being a pain.

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1the limit of a divergent series is infinite and some other limits might not exist (there are shades of convergence, absolute, conditional...)

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1You must have a way, analyytically, to approach a limit (even if you do not actually ever reach it)

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1I am assuming you have studied calculus, the limit concept there is similar.

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0i see . if we say that x> 2 x approaches 2 . what comment would you have?

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0i have studied CAL but in a very mechanical way!

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1You can say it and it implies that the limit is 2 but doesn't say anything about how you got that.

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0do we care how we get there . is that important for us?

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1How do we know that your limit is valid?

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1The limit of 1 + 1/2 +1/4 + 1/8 ......+1/2^n has a limit of 2 Do you believe me?

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0well you told me thats

estudier
 3 years ago
Best ResponseYou've already chosen the best response.1Anyway, 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
 3 years ago
Best ResponseYou've already chosen the best response.1And now I am off to bed, I'm afraid.....

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0visually . dw:1348445954284:dw

hal_stirrup
 3 years ago
Best ResponseYou've already chosen the best response.0thanks you Rock. :)
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