Sequence of rational numbers

[Vlrf]

Hi, I'm struggling with this question, we've just started this topic, I have never done a question similar to this and couldn't find anything in my notes. Any help at all on how to go about problems like this would be great. Thankyou!
Give an example of a sequence of positive rational numbers {qn}^∞_n=1 such that the following statement holds: ∀K > 0 there exists n > 1 such that |qn-qn+1| >K.

 

[HallsofIvy]

Do you understand what "∀K > 0 there exists n > 1 such that |qn-qn+1| >K" means? It means the distance between two consecutive number becomes arbitrarily large. Suppose you define \(\displaystyle q_0= 0\) and then \(\displaystyle q_{n+1}= q_n+ n\). That gives \(\displaystyle q_1= 0+ 1= 1\), \(\displaystyle q_2= 1+ 2= 3\), \(\displaystyle q_3= 3+ 3-= 6\), \(\displaystyle q_4= 6+ 4= 10\), etc.

 

[Vlrf]

Ok I think I understand that, thankyou!