Real Analysis

  • #1

Homework Statement


Prove sequence ((-1)^m)m diverges.

Homework Equations



for all epsilon greater than zero, there exists a natural number M such that for all natural numbers m greater than or equal to M, Ix_m-xI is less than or equal to epsilon.[/B]


The Attempt at a Solution



Assume it converges and consider epsilon to be 1/2, so there is an M such that I((-1)^m)m-LI is less than or equal to epsilon for all m greater than or equal to M. Now consider m to be 2M, Why is m greater than or equal to 1/2 for when m=2M? Just help me with this part, and not anything else, please.
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
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Why is m greater than or equal to 1/2 for when m=2M?
Did you mean to ask why ##(-1)^m m \ge 1/2## when ## m = 2M##?
 
  • #3

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