# Preliminary Test of Alternating Geometric Series

1. Apr 2, 2016

### The-Mad-Lisper

1. The problem statement, all variables and given/known data
$$\lim_{n \to \infty}\frac{(-1)^{n+1} \cdot n^2}{n^2+1}$$

2. Relevant equations
$$\lim_{n \to \infty}a_n \neq 0 \rightarrow S \ is \ divergent$$

3. The attempt at a solution
I tried L'Hopital's rule, but I could not figure out how to find the limit of that pesky $(-1)^{n+1}$.

Edit: This is not actually a geometric series, disregard that part of the title.

2. Apr 2, 2016

### Ray Vickson

Is there a question somewhere here? You seem to have arrived at the correct conclusion for the correct reason, so what are you unsure about?

3. Apr 3, 2016

### The-Mad-Lisper

Computing the derivative of an exponential function results in another exponential function, which doesn't really help when it comes to using L'Hopitals rule.

4. Apr 3, 2016

### micromass

This is a rule for series. Why is this relevant? There are no series in your post.

5. Apr 3, 2016

### HallsofIvy

Your post is very confusing! You title this "alternating geometric series" but appear to be asking about a "sequence" rather than a "series". Further this is not a "geometric" series or sequence. If the "problem statement" is to determine whether or not the series $\sum_{n=0}^\infty \frac{(-1)^n n^2}{n^2+ 1}$ converges then you should know that an alternating series, $\sum_{n=0}^\infty a_n$, converges if and only if the sequence $a_n$ converges to 0. Finally, you ask about the limit of $(-1)^n$. That sequence does not converge so has no limit but that is irrelevant to this problem.

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