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## Homework Statement

Why does this series diverge?

## Homework Equations

[itex]\sum_{n}^{\infty }\frac{-1^{(2n+2)}}{n+1}[/itex]

## The Attempt at a Solution

I must be missing a rule with the -1 sign.

My logic is that for all n, the numerator = 1 since anything to the power of 2 is even and adding the 2 doesn't change the sign either. So if the numerator is always 1 and the denominator grows without bound so by the alternating series test since, L = 0 and the series is decreasing, the series should converge... My math book and maple says different though :(

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