Bonjour,
ex 1:
[tex]1)\\\\V_0=900\\V_1=V_0-V_0*\dfrac{15}{100}=V_0*0.85=765\\V_2=V_1*0.85=V_0*0.85*0.85=V_0*0.85^2=650.25\\\\[/tex]
[tex]2)\\
V_{n+1}=V_n*0.85\\
\textrm{la suite est d\' ecroissante.}\\3)[/tex]
[tex]3)\\\\
\boxed{V_n=V_0*0.85^n}\\\\
V_{2019-2015}=V_{4}\\\\\quad\ =900*0.85^4\\\\\quad\ =900*0.52200625\\\\
\quad\ =469.805625\\\\\quad\ \approx{470}[/tex]
ex 2:
[tex]1a)\\p_0=60*3.20=192\\p_1=p_0*1.06=203.52\\1b)\\
(p_n)\ est\ g\' eom\' etrique\ de\ raison\ 1.06[/tex]
[tex]2a)\\
p_0+p_1+...+p_14\ est\ le\ prix\ des\ cigarettes\ fum\' ees\ de\ 2000\ \` a \ 2014\\[/tex]
[tex]2b)\\p_0+p_1+...+p_14=\sum_{i=0}^{14}(p_i)\\\\
\quad\ =p_0+p_0*1.06+p_0*1.06^2+p_0*1.06^3+...+p_0*1.06^{14}\\\\
\quad\ =p_0*(1+1.06+1.06^2+1.06^3+...+1.06^{14}\\\\
\quad\ =p_0*\dfrac{1.06^{15}-1}{1.06-1}\\\\\quad\ =192*\dfrac{1,396558193...}{0.06}\\\\\quad\ =4468.986217919...\\\\\quad\ \approx{4468.99}[/tex]
