Question

1+2+3+4+...+109
2+4+61...+2008
1+3+5+...2009

Answer 1

Răspuns:

Explicație pas cu pas:

1 + 2 + 3 + 4 + ..... + 109 = 5 995

= 109 × ( 1 + 109 ) : 2 =

= 109 × 110 : 2 =

= 109 × 55 =

= 5 995

__________________________

2 + 4 + 6 + 8 + .... + 208 =10 920

= 2×1 + 2× 2 + 2×3 + 2×4 + .... + 2×104 =

->  il dau factor comun pe 2

= 2 × ( 1 +2+3+4 + ....... + 104 ) =

= 2 × 104 × ( 1 + 104) : 2 =

= 104 × 105 =

= 10 920

___________________________

1 + 3 + 5 + ....... + 2009 =

→ stabilesc cati termeni are suma:

(2009 - 1 ) : 2 + 1 = 2008 : 2 + 1 = 1004 + 1 = 1005 termeni are suma cu ratia 2

= 1005 × ( 1 + 2009 ) : 2 =

= 1005 × 2010 : 2 =

= 1005 × 1005 =

= 1 010 025