Question

Prove that 2n+1 > (n + 2) · sin(n) for all positive integers n.

Answer 1

$2n+1>n+2$ for $n>1.$

Since $|sin(n)|\le1$, $2n+1>(n+2)sin(n)$ for $n>1.$

For n=1, $sin(1)<1,$ and $3>3*sin(1)$.

Therefore, 2n+1 > (n + 2) · sin(n) for all positive integers n.