Question

Calculati sumele urmatoare in metoda lui GAUSS
A.) S=2+4+7+...+100
B.) T=1+3+5+...+99
C.) P=2+5+8+11+14+...+98

DAU COROANA !! RPD
VA ROG!

Answer 1

a)
S = 2 + 4 + 6 +...+ 100
S = 2×(1+2+3+...+50)
S = 2×50 × 51: 2
S = 50 × 51
S = 2 550

b)
S = 1 + 3 + 5 +...+ 99
S = 2×0+1 + 2×1+1 + 2×2+1 +...+ 2×49+1
S = 2×(0+1+2+...+49) + 1 + 1 + 1+...+1 de 50 ori
S = 2×49 × 50 : 2 + 1 ×50
S = 98 × 25 + 50
S = 2450 + 50
S = 2500

c)
S = 2 + 5 + 8 + 11 + 14 +...+ 98
S = 3×0+2 + 3×1+2 +3×2+2 +3×3+2 + 3×4+2 +...+ 3×32+2
S = 3×(0+1+2+3+4+...+32) + 2+2+2+...+2 de 33 ori
S = 3 × 32 × 33 : 2 + 2 × 33
S = 99 × 16 + 66
S = 1584 + 66
S = 1 650