calculati suma s= -1+2-3+-5+6-7.....-2011+2012

Răspuns:

Explicație pas cu pas:

• primul mod de rezolvare

S = - 1 + 2 - 3 + 4 - 5 + 6 - 7 + .......- 2011 + 2012

S = ( -1+2)+(-3+4)+(-5+6) + .......+(-2011+2012)

S = 1 + 1 + 1 + 1 + ....... + 1

-> sunt 2012 termeni

-> avem 2012 : 2 = 1006 sume de cate 1

S = (2012:2) × 1

S = 1006 × 1

S = 1006

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• al doilea mod

S = ( - 1 - 3 - 5-......-2011) + ( 2+4+6+8+.....+2012)

S = - ( 1+3+5+.....+2011) + 2 ×(1+2+3+.....+ 1006)

1+3+5+....+2011 => suma are (2011-1):2+1 = 2010:2+1=1006 termeni

S = - 1006 × ( 1+2011):2+ 2×1006 × (1+1006): 2

S = - 1006 × 1006 + 1006 × 1007

S = - 1006 × ( 1006 - 1007)

S = - 1006 × ( - 1 )

S = 1006