Question

cum pot calcula 7+14+21+...+210

Answer 1

-notez suma respectiva cu S
S=7+14+21+...+210 observam ca putem da in factor pe 7 deci
S=7(1+2+3+...+30) in paranteza avem o suma gauss deci sumele gauss au formula:$\frac{n(n+1)}{2}$ deci
S=7($\frac{30(30+1)}{2}$)
S=7·465 deci S=3255

Answer 2

$\displaystyle 7+14+21+...+210=7(1+2+3+...+30)= \\ =7 \cdot \frac{30(30+1)}{2} =7 \cdot \frac{30 \cdot31}{2} =7 \cdot \frac{930}{2} =7 \cdot 465=3255$