Question

Calculati sumele:
A) 1+2+3+....+120
B) 36+37+38+....+98
C) 5+10+15+...+200

Answer 1

Suma lui Gauss:1+2+3+...+n=[n(n+1)]/2
A) =120*121/2=60*121=7260
B) Lipsește 1+2+2+...+35 din sumă.
S=36+37+38+...+98-(1+2+3+...+35)
S=98*99/2-(35*36)/2
S=49*99-35*18
S=4851-630
S=4221
C) 5 e factor comun.

S=5(1+2+3+...+40)
S=5*40/41/2
S=5*20*41
S=100*41
S=4100