Question

Efectuați:1. 2+4+6+....+80
2. 10+20+30+.....580
3. 7+14+21+......+700

Answer 1

$\displaystyle a).2+4+6+...+80=2(1+2+3+...+40)=2 \times \frac{40(40+1)}{2} = \\ \\ =2 \times \frac{40 \times 41}{2} =\not 2 \times \frac{1640}{\not2} =1640 \\ \\ b).10+20+30+...+580=10(1+2+3+...+58)= \\ \\ =10 \times \frac{58(58+1)}{2} =10 \times \frac{58 \times 59}{2} =10 \times \frac{3422}{2} =10 \times 1711=17110$

$\displaystyle c).7+14+21+...+700=7(1+2+3+...+100)= \\ \\ =7 \cdot \frac{100(100+1)}{2} =7 \times \frac{100 \times 101}{2} =7 \times \frac{10100}{2} =7 \times 5050=35350$