Question

Fie numerele a= -1-3-5-...-99 si
b= 100+98+96+...+2
atunci :
a. a-b ≠ 5050
b. b-a ≠5050
c. a+b≠50

Answer 1

100+98+96+....+2=2×50+2×49+2×48+.....+2×1
2(1+2+3+....+50)=2×50×51÷2=50×51=2550
-(1+3+5+......+99)=-(2×-1+2×2-1+2×3-1+...2×59-1)
=-2(1+2+3+....+50)-1×50
=-2×50×51÷2-50
=-50×51-50=-2600
-2600-2550=-5150
2550+2600=5150
-2600+2550=-50 cam asa cred ca este