Bonsoir,
[tex]u_0=150000\\
1)\\
u_1=u_0* 0.98=150000*0.98=147000\\
u_2=u_1* 0.98=u_0*0.98^2=150000*0.98^2=144060\\
u_{n+1}=u_n*0.98
3)\\
\boxed{u_n=u_0*0.98^n}\\\\
4)\\
(u_n) \ est\ positive\ et\ d\'ecroissante.\\\\
u_{24}=150000*0.98^{24}=92367,05047...\\\\
6)\\
u_0*0.98^n\ \textless \ 100000\\\\
0.98^n\ \textless \ \frac{100000}{150000} \\\\
0.98^n\ \textless \ \dfrac{2}{3} \\\\
n*ln(0.98)\ \textless \ ln(2)-ln(3)\\\\
n\ \textgreater \ \dfrac{ln(2)-ln(3)}{ln(0.98)} \\\\
n\ \textgreater \ 20.06984...\\\\
\boxed{n \geq 21}\\\\
[/tex]
