Question

10+20+30+40..........+900

Answer 1

10 + 20 + 30 + 40 + ......... + 900 =
10(1 + 2 + 3 + 4 +........+ 90) =
10 * 91 * 90 : 2 = 
910 * 45 = 
40 950

Answer 2

$\displaystyle 10+20+30+40+..........+900= \\ \\ \text{factor comun pe 10} \\ \\ 10(1+2+3+4+...+90)= \\ \\ \text{Suma lui Gauss in paranteza} \\ \\ \frac{n(n+1)}{2} = \frac{90(90+1)}{2}= \frac{\not90\cdot91}{\not2}= 45\cdot91=4095 \\ \\ \text{de retinut ca suma se aplica la sirul 1+2+3+..si n e ultimul nr din sir} \\ \\ 10 \cdot 4095= \boxed{40.950}$