# Sequence question

• Apr 25th 2012, 05:32 AM
lebanon
Sequence question
Given the sequence (Un) defined by Un=(2n-3)/(n+3) for any natural number n
show that Un<2 for any natural number n , knowing that (Un) is strictly increasing
• Apr 25th 2012, 05:48 AM
HallsofIvy
Re: Sequence question
It's pretty close to trivial isn't it? For what n is $\frac{2n- 3}{n+1}\le 2$ true? Just solve that inequality.