(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

State whether or not the sequence {a_n} = n+[(-1)^n]/n is monotone or not and justify.

2. Relevant equations

3. The attempt at a solution

It clearly appears to be monotone increasing, so I attempt to prove this. I've tried using induction and tried to prove that {an+1} -{an} >= 0. However, I've got it down to proving n(n-1)>0 for n>1, but I'm not sure how to prove this using just the basic axioms of analysis.

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# Monotonicity of n + (-1)^n/n

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