Determining of a sequence is convergent or divergence

[nlsherrill]

Homework Statement

For x$_{n}$ given by the following formula, establish either the convergence or divergence of the sequence $X = (x_{n})$

$x_{n} := (-1)^{n}n/(n+1)$

Homework Equations

The Attempt at a Solution

This is for my real analysis class. I tried to use the squeeze theorem, but didn't get anywhere with it. I know $(-1)^{n}$ is divergent, and n are divergent sequences but I haven't been able to use many theorems in the section because most of them are assuming something about a convergent sequence(and I need to show if it is or isn't)

Any ideas?

Thanks for lookingedit:

*Note: I have already shown that $x_{n} := (-1)^{n}/(n+1)$ converges to zero using the squeeze theorem, but the extra "n" in the numerator is messing me up with this one..

 

[Mark44]

Homework Statement

For x$_{n}$ given by the following formula, establish either the convergence or divergence of the sequence $X = (x_{n})$

$x_{n} := (-1)^{n}n/(n+1)$

Homework Equations

The Attempt at a Solution

This is for my real analysis class. I tried to use the squeeze theorem, but didn't get anywhere with it. I know $(-1)^{n}$ is divergent, and n are divergent sequences but I haven't been able to use many theorems in the section because most of them are assuming something about a convergent sequence(and I need to show if it is or isn't)

Any ideas?

Thanks for looking


edit:

*Note: I have already shown that $x_{n} := (-1)^{n}/(n+1)$ converges to zero using the squeeze theorem, but the extra "n" in the numerator is messing me up with this one..

Write out about a dozen terms in the sequence. That should give you a better idea about what this one is doing.

 

[nlsherrill]

Write out about a dozen terms in the sequence. That should give you a better idea about what this one is doing.

well sure I can do that and tell that it is heading towards -1 and 1, i.e. its divergent, but I was assuming the problem was asking some kind of use of a theorem to prove its divergent

 

[Mark44]

You could use the definition of a divergent sequence (the negation of the definition of a convergent sequence).