Proving Divergence of ((-1)^m)m

[Mathematicsresear]

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.

 

[Stephen Tashi]

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 $m = 2M$?

 

[Mathematicsresear]

Did you mean to ask why $(-1)^m m \ge 1/2$ when $m = 2M$?

no