Question

Va rog doar pentru una macar sa imi aratati cum se rezolva
a)10+20+30+........+800
b)13+26+39+.........715

Answer 1

a)

10+20+30+........+800 =

dam factor comun  pe 10

10 × (1 + 2 + 3 + ....+ 80) =

10 × 80 x (80 + 1) : 2=

10 × 80 × 81 : 2  =

400 x 81 =

32400  

b)

13+26+39+.........715 =

dam factor comun pe 13

13 × (1 + 2 + 3 + ...+ 55 ) =

13 × 55 × (55+1) : 2 =

13 × 55 × 56 : 2 =

13 × 55 × 28 =

20020

1 + 2 + 3 + ......+ n =

S = n × (n + 1) : 2  unde n = ultimul numar al sirului

Answer 2

= 10x(1+2+3+......+80)

= 10 x ( 80 x 81 :2) =

=> 10x 40 x 81

=> 400 x 81 = 32400


B)=

13x(1+2+3+.......+55) =

=> 13 x( 55x56:2) =

=> 13 x 55 x 28 =

=> 715 x28 = 20020