Question

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 ??

Answer 1

thanks of viewing.

Answer 2

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

Answer 3

yes. it is.

Answer 4

so what do you think of my question?.

Answer 5

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

Answer 6

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

Answer 7

Convergence

Answer 8

so your saying if a series Converges it partial sums exists

Answer 9

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

Answer 10

yes

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

If the series converges then you can take a limit

Answer 16

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.

Answer 17

am sorry am being a pain.

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

i have studied CAL but in a very mechanical way!

Answer 23

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

Answer 24

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

Answer 25

How do we know that your limit is valid?

Answer 26

The limit of 1 + 1/2 +1/4 + 1/8 ......+1/2^n has a limit of 2

Do you believe me?

Answer 27

well you told me thats

Answer 28

Ok, it's not 2 it's 3

Answer 29

no its not !

Answer 30

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

Answer 31

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

Answer 32

visually .