# Thread: Comparison Theorem

1. ## Comparison Theorem

1. $\sum_{n = 1}^{\infty} \frac{n - 1}{n4^{n}}$

2. $\sum_{n = 1}^{\infty} \frac{n^{2} - 5n}{n^{3} + n + 1}$

I don't really understand how to use the comparison theorem.

2. Originally Posted by FalconPUNCH!
1. $\sum_{n = 1}^{\infty} \frac{n - 1}{n4^{n}}$
Idea: $\left(1 - \frac1{n}\right) < 1 \Rightarrow \sum_{n = 1}^{\infty} \frac{n - 1}{n4^{n}} < \sum_{n = 1}^{\infty} \frac1{4^{n}}$