Question

1. Calculati suma : 1+2 la puterea 1+2 la puterea 2+2 la puterea 3+...+2 la puterea 2000​

Answer 1

 

$\displaystyle\bf\\Folosim~formula:\\\\k^0+k^1+k^2+k^3+...+k^n=\frac{k^{n+1}-1}{k-1}\\\\\\1+2^1+2^2+2^3+...+2^{2000}=\\\\=2^0+2^1+2^2+2^3+...+2^{2000}=\\\\=\frac{2^{2000+1}-1}{2-1}=\boxed{\bf2^{2001}-1}$