Question

Calculati
a) (2+4+....200):[(4+8+...+100):13]
b) (8+16+...+344):(4+8+...+172)

Answer 1

$\displaystyle a).(2+4+...+200):[(4+8+...+100):13]= \\ \\ =2(1+2+...+100):\{[4(1+2+...+25)]:13\}= \\ \\ =2 \cdot \frac{100(100+1)}{2} :\left(4 \cdot \frac{25(25+1)}{2}:13 \right) = \\ \\ =2 \cdot \frac{100 \cdot 101}{2} :\left(4 \cdot \frac{25 \cdot 26}{2} :13 \right)=\not 2 \cdot \frac{10100}{\not 2} :\left(4 \cdot \frac{650}{2} :13 \right)= \\ \\ =10100:\left(4 \cdot 325:13 \right)=10100:(4 \cdot 25)=10100:100=101$

$\displaystyle b).(8+16+...+344):(4+8+...+172)= \\ \\ =8(1+2+...+43):4(1+2+...+43)=8:4=2$