Question 54
Let $t \geqslant \frac{1}{2}$ be a real number and $n$ a positive integer. Prove that
$$
t^{2 n} \geqslant (t-1)^{2 n} + (2 t-1)^{n}
$$
$$
t^{2 n} \geqslant (t-1)^{2 n} + (2 t-1)^{n}
$$
MathNet 2000 — Math Olympiad Vault Question 54
Math Olympiad Vault · MathNet 2000 — Math Olympiad Vault