👤

fie suma de numere naturale consecutive S=6+7+8+.......+74. Sa se arate ca S=2760

Răspuns :

S=6+7+8+...+74

S = (1+2+3+...+74) - (1+2+3+..+5)

S = 74 × (74+1) : 2 - 5×(5+1) : 2

S = 37 × 75 - 5 × 6 : 2

S = 2 775 - 15

S = 2 760
S=6+7+8+......+74
Aflam cati termeni avem prima data
74-6+1=68+1=69
69×(6+74):2=
=69×80:2=
=69×40=2760
S=2760(A)