Math Help - How is problem 4 done?

1. 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

2. Originally Posted by zhupolongjoe
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
For 1., we can test for ABSOLUTE convergence.

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

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