Homework Help: Sequences HELP

When trying to determine if a sequence converges it needs to approach a certain number. By pluging in numbers for the value of n you'll notice that

Cn = [(-1)^n * 1/n!]

will jump back and fourth between positive and negative values, and therefore isn't approaching a single value. You then need to find a graph both above and below that sequence that converge, you do this by the squeeze theorem.

If you graph all three of those sequences you'll notice that Cn = [(-1)^n * 1/n!] lies in-between. You can therefore say that because

1/2^n

and

-1/2^n

converge, the value in-between them converges also. What would that be the?

 

Yes all the values converge to zero. I really don't like to use the squeeze theorem, whenever I have to use it it's just by trial and error.

There should however be another theorem which relates to sequences that jump back and fourth. It's called the Absolute Value Theorem, which would allow you to more easily find the convergence of a sequence like this.