Question 56
Let $a$, $b$, $c$ be positive real numbers with $a + b + c = 1$.
Prove that
$$
\frac{a}{2a+1} + \frac{b}{3b+1} + \frac{c}{6c+1} \le \frac{1}{2}.
$$
When does equality hold?
Prove that
$$
\frac{a}{2a+1} + \frac{b}{3b+1} + \frac{c}{6c+1} \le \frac{1}{2}.
$$
When does equality hold?