I came across an inequality and I can't seem to solve it.
For all natural numbers $m, n$,
$$\frac{1}{\sqrt[n]{1+m}}+\frac{1}{\sqrt[m]{1+n}} \ge 1.$$
I tried isolating roots and then raise both sides to power of m
(or n
) but that didn't lean anywhere.
Can anyone show me what would be the way to go about this?
$\forall$
? $\endgroup$