Bonsoir,
5b)
[tex]a_0= \dfrac{5}{4} \\
a_1= a_0+1*\dfrac{1}{2} \\
a_2= a_0+2*\dfrac{1}{2} \\
...\\
a_{n-1}= a_0+(n-1)*\dfrac{1}{2} \\\\
\sum_{i=0}^{n-1}{a_i}=a_0+a_1+a_2+...+a_{n-1}\\\\
=a_0+(a_0+1*\dfrac{1}{2} )+(a_0+2*\dfrac{1}{2} )+(a_0+3*\dfrac{1}{2} )+...\\
+(a_0+(n-1)*\dfrac{1}{2} )\\\\
=a_0*n+\dfrac{1}{2}(0+1+2+3+...+(n-1))\\
=\dfrac{5}{4}*n+\dfrac{1}{2}\dfrac{(n-1)*n}{2}\\
=\dfrac{5}{4}*n+\dfrac{n^2}{4}-\dfrac{n}{4}\\
=\dfrac{n^2}{4}+n\\
Ici\ n-1=20\ d\'\ ou\ n=21\\\\
Aire=\dfrac{21^2}{4}+21
[/tex]
5b')
[tex] \int\limits^0_{21} {(\dfrac{x}{2}+1)} \, dx =
\left[\dfrac{x^2}{4}+x\right] _0^{21}=\dfrac{21^2}{4}+21[/tex]
