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 ??

- anonymous

- jamiebookeater

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- anonymous

thanks of viewing.

- anonymous

Well, it's convenient for looking at convergence and limits, no?

- anonymous

yes. it is.

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## More answers

- anonymous

so what do you think of my question?.

- anonymous

Well, we can sum up the series (if the limit of partial sums exists)

- anonymous

we can? how do we know if the limit of partial sums exists?

- anonymous

Convergence

- anonymous

so your saying if a series Converges it partial sums exists

- anonymous

Well, if a series diverges, there wouldn't be any convergence, right?

- anonymous

yes

- anonymous

And you wouldn't be able to add it up however hard you tried

- anonymous

yes BUT because its a infinite series whether it converges or diverges we cant sum it all up?

- anonymous

That's what I'm saying, if it converges then you can (usually) add it up (analytically).

- 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

If the series converges then you can take a limit

- 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

am sorry am being a pain.

- anonymous

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

- anonymous

You must have a way, analyytically, to approach a limit (even if you do not actually ever reach it)

- anonymous

I am assuming you have studied calculus, the limit concept there is similar.

- anonymous

i see . if we say that x-----> 2 x approaches 2 . what comment would you have?

- anonymous

i have studied CAL but in a very mechanical way!

- anonymous

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

- anonymous

do we care how we get there . is that important for us?

- anonymous

How do we know that your limit is valid?

- anonymous

The limit of 1 + 1/2 +1/4 + 1/8 ......+1/2^n has a limit of 2
Do you believe me?

- anonymous

well you told me thats

- anonymous

Ok, it's not 2 it's 3

- anonymous

no its not !

- 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

And now I am off to bed, I'm afraid.....

- anonymous

visually . |dw:1348445954284:dw|

- anonymous

thanks you Rock. :)

- anonymous

G'night:)

- anonymous

you too

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