I'm trying to investigate the boundness of the set:
${x\in \mathbb{R},x=\frac{n^2-1}{n(n+1)}*\sin{\frac{2^n}{n+3}}-\frac{(-1)^n}{n^2+n+1}*\cos{\frac{(-1)^n*n}{3^n}}, n \in \mathbb{N}}$
I upper-bounded it by it's absolute values and upper bounded the trigonometric functions and by the division of 1 and got the following function:
$\leq n^2+2$
Therefore I determined, that the set has no upper bounds. However, what can I tell about the lower bounds? How do I investigate the lower bounds?
Thanks