<s>[INST] Find all $n$ for which $2^n \ge (n+1)^2$ 
Find all of the elements of $X= \{ n \in \mathbb N: 2^n \ge (n+1)^2\}$

Could someone give me a hint to nudge me in the right direction?
 [/INST] $\color{green}{2^0=1\ge(0+1)^2=1}$ ?*
$\color{red}{2^1=2\ge(1+1)^2=4}$ ?
$\color{red}{2^2=4\ge(2+1)^2=9}$ ?
$\color{red}{2^3=8\ge(3+1)^2=16}$ ?
$\color{red}{2^4=16\ge(4+1)^2=25}$ ?
$\color{red}{2^5=32\ge(5+1)^2=36}$ ?
$\color{green}{2^6=64\ge(6+1)^2=49}$ ?
$\color{green}{2^7=128\ge(7+1)^2=64}$ ?
$\color{green}{2^8=256\ge(8+1)^2=91}$ ?
$\color{green}{2^9=512\ge(9+1)^2=100}$ ?
...
*whether $0$ is considered natural or not is a matter of convention.
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