Which is larger, $99^{100}$ or $100^{99}$?
Which is larger, $999^{1000}$ or $1000^{999}$?
Or more generally, for $n$ any natural number: which is larger, $n^{n+1}$ or $(n+1)^n$?
Please do not use a computer, calculator, or any electronic aid to work out the answer for any specific cases of $n$. You should be able to solve this puzzle purely by mathematical reasoning and without calculations, using a computer only to read the question and type the answer :-)