If you could just help me out with problem 4 here, that would be great. Thanks

http://math.rutgers.edu/~jsosa/Courses/Math152/w10.pdf

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- Apr 11th 2009, 05:50 PM #1

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## How is problem 4 done?

If you could just help me out with problem 4 here, that would be great. Thanks

http://math.rutgers.edu/~jsosa/Courses/Math152/w10.pdf

- Apr 11th 2009, 06:00 PM #2
For 1., we can test for ABSOLUTE convergence.

So if $\displaystyle \sum_{n = 2}^\infty{\frac{1}{n(\ln{n})^2}}$ converges, so does $\displaystyle \sum_{n = 2}^\infty{\frac{(-1)^n}{n(\ln{n})^2}}$.

Notice that $\displaystyle \int_2^\infty{\frac{1}{x(\ln{x})^2}\,dx}$ is a relatively easy integral to solve (just use a u-substitution). So you could do an integral test.

Edit: Should have read your original post more carefully - you've already done this one