Question

calculati:

10+20+30+40+...+90=?
100+200+300+...+1000=?​

Answer 1

10*1+10*2+10*3+10*4+...+10*9=10(1+2+3+4...+9)=10*9*(9+1)/2=10*9*10/2=10*9*5=450

100*1+100*2+100*3+...+100*10=100(1+2+3+...+10)=100*10*(10+1)/2=100*10*11/2=100*5*11=5500

Suma lui Gauss 1+2+3+...+n=[n*(n+1)]/2

Pentru a calcula aceste sume am dat factor comun 10, respectiv, 100, apoi am aplicat formula sumei lui Gauss pentru fiecare paranteza.

Answer 2

Răspuns:

Explicație pas cu pas:

10 + 20 + 30 + 40 +. ..+ 90 / : 10

10 × ( 1+2+3+4 +. ....+9 ) =

10 × 9 × ( 9+1 ) : 2 =

10 × 9 × 10 : 2 =

90 ×10 : 2 =

900 : 2 = 450

100 + 200 + 300 +. ...+ 1000 / : 100

100 × ( 1 + 2 + 3 +. . .+ 10 ) =

100 × 10 × (10+1) : 2 =

100 × 10 × 11 : 2 =

1000 × 11 : 2 =

11.000 : 2 =

5500