## 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 ??

1. hal_stirrup

thanks of viewing.

2. estudier

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

3. hal_stirrup

yes. it is.

4. hal_stirrup

so what do you think of my question?.

5. estudier

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

6. hal_stirrup

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

7. estudier

Convergence

8. hal_stirrup

so your saying if a series Converges it partial sums exists

9. estudier

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

10. hal_stirrup

yes

11. estudier

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

12. hal_stirrup

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

13. estudier

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

14. hal_stirrup

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

15. estudier

If the series converges then you can take a limit

16. hal_stirrup

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.

17. hal_stirrup

am sorry am being a pain.

18. estudier

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

19. estudier

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

20. estudier

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

21. hal_stirrup

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

22. hal_stirrup

i have studied CAL but in a very mechanical way!

23. estudier

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

24. hal_stirrup

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

25. estudier

How do we know that your limit is valid?

26. estudier

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

27. hal_stirrup

well you told me thats

28. estudier

Ok, it's not 2 it's 3

29. hal_stirrup

no its not !

30. estudier

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

31. estudier

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

32. hal_stirrup

visually . |dw:1348445954284:dw|

33. hal_stirrup

thanks you Rock. :)

34. estudier

G'night:)

35. hal_stirrup

you too