Question

Calculați:
a) -50-49-...-1+0+1+...+51.
b) -1-2-...-100.
c) -2-4-6-...-100.
d) 1-2+3-4+5-6+...+99-100.

Answer 1

a) -50-49-...-1+0+1+...+51=-(1+2+....+50)+(1+2+...+51)=
=-50×51/2+51×52/2=51/2 × (52-50)=51/2× 2=51
b) -1-2-...-100=-(1+2+...+100)=-100×101/2=-50×101=-5050
c) -2-4-6-...-100=-2(1+2+...+50)=-2×50×51/2=-50×51=-2550
d) 1-2+3-4+5-6+...+99-100 =-1-1+....-1=-50