Question

Calculati folosind eventual proprietățile adunarii: S1= - 1+2-3+4-5+6-......-15+16-17+18; S2= - 1-2+3+4-5-6+7.....-14+15+16-17-18

Answer 1

S₁= (2+4+6+....+18) - ( 1+3+5+....+17) =

S₁= 2×(1+2+....+9) −[(1+2+3+4+....+17)−(2+4+....16)]

S₁= 2×9×10/2 −[ 17×18/2 − 2×8×9/2] =

S₁= 9×10− ( 17×9 − 8×9)=

S₁= 9×10 − 9×(17-8)=

S₁= 10×9 − 9× 9 =

S₁= 9( 10−9)= 9×1= 9