Question

Sa se rezolve ecuatia 11+12+...+100=5(1000x-1)

Answer 1

facem un artificiu ca sa facem Gauss:
adaugam 1+2+3+...+10 si apoi il scadem

(1+2+3+4+5+6+7+8+9+10+11+....+100)-(1+2+3+..+10)=5(1000x-1)
Facem Gauss separat
100*101/2-10*11/2=5(1000x-1)
10100-110/2=5000x-5
9990/2=5000x-5
4995=5000x-5
5000x-5=4995
5000x=4995+5
5000x=5000
x=5000:5000
x=1

Answer 2

1+2+3+.......+100 - (1+2+3+.....10) = 5(1000x - 1)
100·101/2 - 10·11/2 = 5(1000x -1)
5050 - 55 = 5000x - 5
5000= 5000x
x=1