- #1

Monte_Cristo

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## Homework Statement

Determine whether the infinite series converge or diverge?

∞

∑ 1/{1+n[(ln n)^2]}

n=0

## Homework Equations

Direct Comparison test

Limit Comparison test

Root test

Ratio test

integral test

## The Attempt at a Solution

Personally, I think that only two methods can work:

1) Manual method - meaning writing down the series and then look at if its converging or diverging.

2) Direct Comparison test - If I compare it directly with the limit of n approaching infinity for 1/n, then my answer comes out to be that the "series diverges

If I use 1/n[(ln n)^2] or else 1/[(ln n)^2] for direct comparison test, I get the same result.

BUT, when I do it the manual way, my answer turns out to be

**CONVERGENT**.

Its so confusing, please help!

Thanks

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