he same job? f a man earns \( \$ 805 \) per week in how many days he will earn \( \$ 1840 \) ? f the cost of 20 chocolates is Rs 360 , what will be the cost of one dozel

\( \sum _ { x \rightarrow 4 } - \operatorname { Lim } _ { x } - 8 \)

d \( \frac{9}{5} \square 1 \frac{2}{5} \)

Maxumezar \( f=5 x+10 y+30 z \quad\left\{\begin{array}{l}4 x+y+z \leq 2 \\ x+y+2 z \leq 2 \\ x \geqslant 0 ; y \geqslant 0 ; z \geqslant 0\end{array}\right. \)

Soit \( n \) un entier naturel. On rappelle que pour tout réel \( q \) différent de 1, \[ \sum_{k=0}^{n} q^{k}=1+q+q^{2}+q^{3}+\ldots+q^{n}=\frac{1-q^{n+1}}{1-q} \] A l'aide de cette égalité, déterminer la limite de la suite \( \left(u_{n}\right) \) dans chacun des cas suivants. 1. \( u_{n}=1+\frac{1}{2}+\frac{1}{4}+\ldots+\frac{1}{2^{n}}=\sum_{k=0}^{n} \frac{1}{2^{k}} \) 2. \( u_{n}=1+\frac{2}{3}+\frac{4}{9}+\ldots+\frac{2^{n}}{3^{n}}=\sum_{k=0}^{n} \frac{2^{k}}{3^{k}} \) 3. \( u_{n}=8+2+\frac{1}{2}+\frac{1}{8}+\ldots+\frac{8}{4^{n}}=\sum_{k=0}^{n} \frac{8}{4^{k}} \)

8) On a road map of Pennsylvania, the distance from Philadelphla to Washington, D.C. is 6.8 centimeters. What is the actual distance between the cities if the map scale is 2 centimeters \( =41 \) miles?