I tried to solve the inequality
$$n\left(\frac{n}{n+1}\right)^n>1,\quad n\in\Bbb N$$
with this code
Solve[x*(x/(1 + x))^x > 1 && x > 0, x, Integers]
but the program said
This system cannot be solved with the methods available to Solve.
My attempt using 'NSolve' failed too. My question: there is a way to solve the inequality?