Răspuns:
Explicație pas cu pas:
1 + 2 + 3 + 4 + ..... + 109 = 5 995
= 109 × ( 1 + 109 ) : 2 =
= 109 × 110 : 2 =
= 109 × 55 =
= 5 995
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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
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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
