grandes-ecoles 2025 Q13

grandes-ecoles · France · centrale-maths1__official Proof Bounding or Estimation Proof
Let $x \geqslant 3$. Show that
$$\pi ( x ) \geqslant \frac { \ln ( 2 ) } { 6 } \frac { x } { \ln ( x ) }$$
One may set $n = \lfloor x / 2 \rfloor$ and use Q12.
Let $x \geqslant 3$. Show that

$$\pi ( x ) \geqslant \frac { \ln ( 2 ) } { 6 } \frac { x } { \ln ( x ) }$$

One may set $n = \lfloor x / 2 \rfloor$ and use Q12.