grandes-ecoles 2025 Q4

grandes-ecoles · France · centrale-maths1__official Binomial Theorem (positive integer n) Prove a Binomial Identity or Inequality

Show that, for all $n \in \mathbb { N } ^ { * }$,
$$\frac { 4 ^ { n } } { 2 n } \leqslant \binom { 2 n } { n } < 4 ^ { n } .$$

Show that, for all $n \in \mathbb { N } ^ { * }$,

$$\frac { 4 ^ { n } } { 2 n } \leqslant \binom { 2 n } { n } < 4 ^ { n } .$$