Soit \(\omega = \exp\frac {2i\pi}n\). Calculer :
1
\(\sum_{k=0}^{n-1} (1+\omega^k)^n\).
2
\(\sum_{k=0}^{n-1}\sum_{\ell=k}^{n-1} C_\ell^k \omega^{k+\ell}\).
Soit \(\omega = \exp\frac {2i\pi}n\). Calculer :
\(\sum_{k=0}^{n-1} (1+\omega^k)^n\).
\(\sum_{k=0}^{n-1}\sum_{\ell=k}^{n-1} C_\ell^k \omega^{k+\ell}\).