Qwertyuiop[]
Junior Member
- Joined
- Jun 1, 2022
- Messages
- 123
Hi, I have a sequence u(n) = [imath]\frac{4n^2+1}{\:n^2+1}[/imath]. And i have to show that this sequence is increasing. I started by writing it in this form: [imath]4-\frac{3}{n^2+1}[/imath] which was the first part of the question. To show if a sequence is increasing, i know that un+1 - un >0. After simplifying the expression get :[imath]\frac{3}{n^2+1}-\frac{3}{\left(n+1\right)^2+1}\:=\:3\left(\frac{1}{n^2+1}-\frac{1}{\left(n+1\right)^2+1}\right)[/imath]. I am not sure how to prove that it is positive.