Year 12s: what will be the first way you research your future options? >>

Limits question

Hello,

I am stuck on this one question that I need to find the limits.

lim
x -> ∞ (-1)^x

( limit of x to infinity, -1 to the power of x )

As I understand (-1)^x is a wave that it is limit to 1 and -1, I'm not sure if this is correct. Can someone explain this please?

Thanks!

Reply 1

poorform

Original post by Mr_Maths_Student

The limit does not exist. Consider sequence a_n=2,4,6,8,.... and b_n=1,3,5,7.... i.e. the even even and odd numbers respectively.

Clearly both sequences tend to infinity but the value of (-1)^x will not be the same for both sequences.

There is a theorem out there that allows you to make such a conclusion.