Question

Sa se arate ca 2(1+3+3^2+...+3^8)<9.

Answer 1

       
$\text{Consider ca enuntul este asa:} \\ 2(1+3+3^2+...+3^8)\ \textless \ 3^9 \\ \text{Rezolvare: } \\ 2(1+3+3^2+...+3^8)= 2 \left( \frac{3^9 -1}{3-1}\right) = 2 \left( \frac{3^9 -1}{2}\right)=\boxed{3^9-1 \ \textless \ 3^9} \\ cctd$