Series Convergence Tests: Arctan and Grouped Terms

[freshman2013]

Homework Statement

1. Determine if arctan(7+1/n)-arctan(7) converges or diverges

2. Determine if 2/1-1/2-1/3+2/4-1/5/-1/6+2/7... converge or diverge

Homework Equations

series tests

The Attempt at a Solution

1.My gut instinct is to do limit comparison test w/ 1/n, and it worked and I got divergent, but I really don't get why.
2. I did a similar problem in which we group every 3 terms. However, in class, the 2nd and 3rd terms were >0 and every third term combined made a divergent series, so comparision test yields divergent. But in this series, the 2nd and 3rd terms would make the series 0 to inf 2/(3n-2) smaller and it's inconclusive whether smaller than divergent is convergent or divergent.

 

[Dick]

Homework Statement

1. Determine if arctan(7+1/n)-arctan(7) converges or diverges

2. Determine if 2/1-1/2-1/3+2/4-1/5/-1/6+2/7... converge or diverge

Homework Equations

series tests

The Attempt at a Solution

1.My gut instinct is to do limit comparison test w/ 1/n, and it worked and I got divergent, but I really don't get why.
2. I did a similar problem in which we group every 3 terms. However, in class, the 2nd and 3rd terms were >0 and every third term combined made a divergent series, so comparision test yields divergent. But in this series, the 2nd and 3rd terms would make the series 0 to inf 2/(3n-2) smaller and it's inconclusive whether smaller than divergent is convergent or divergent.

You need to show some more of your work to get an answer. How did get a comparison with 1/n. And for the second one what's the expression for the sum of the 3 grouped terms in terms of n? Do some algebra to combine them.