Question

Efectuati(12+24+36+...+444):(6+12+18+...+222)=

Calculati(4+8+12+...+2012):(2+4+6+...+1006)=

Answer 1

1)
(12 + 24 + 36 +...+ 444):(6 + 12 + 18+...+222)=

12(1 + 2 + 3 + ... + 37) : 6(1 + 2 + 3 + ... + 37) =

(1 + 2 + 3 + ... + 37)-suma Gauss, are termenii consecutivi si suma incepe cu 1, are formula de calcul S= [(n(n+1)]:2

 (1 + 2 + 3 + ... + 37)× 12 : 6 =

(37 + 38 : 2) × 2 =

(37 + 19) × 2 =

56 × 2 =

(12 + 24 + 36 +...+ 444):(6 + 12 + 18+...+222) = 112

2)
(4 + 8 + 12+...+2012):(2 + 4 + 6 +...+ 1006)=

=4×(1 + 2 + 3 +...+503): 2×(1 + 2 + 3 +...+ 503)

=4× (503×504)/2 : 2× (503×504)/2

=2×(503×504):(503×504)

(4 + 8 + 12+...+2012):(2 + 4 + 6 +...+ 1006)= 2