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thanks of viewing.

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

yes. it is.

so what do you think of my question?.

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

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

Convergence

so your saying if a series Converges it partial sums exists

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

yes

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

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

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

If the series converges then you can take a limit

am sorry am being a pain.

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

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

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

i have studied CAL but in a very mechanical way!

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

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

How do we know that your limit is valid?

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

well you told me thats

Ok, it's not 2 it's 3

no its not !

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

visually . |dw:1348445954284:dw|

thanks you Rock. :)

G'night:)

you too