Saturday 16 August 2014

real analysis - Prove that a conditionally convergent series has an infinity of positive terms and an infinity of negative terms.

The book I am using for my Advance Calculus course is Introduction to Analysis by Arthur Mattuck.




Prove that a conditionally convergent series has an infinity of positive terms and an infinity of negative terms.



This is my rough proof to this question. I was wondering if anybody can look over it and see if I made a mistake or if there is a simpler way of doing this problem. I want to thank you ahead of time it is greatly appreciated.So lets begin.



Proof:



enter image description here

-

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...