Question

Calculați sumele după model
S = 1 + 2 + ...... 478
S = 1 + 2 + ...... 2000
S = 1 + 2 + 3 + ...... 170
S = 26 + 27 + ........ 175
B) 1 + 2 + 3 + ...... + 73

Answer 1

S =1+2+475=478
S = 1+2+1997=2000
S = 1+2+3+164=170
S = 26+27+122=175
B) scuze nu pricep la B

Answer 2

S=1+2+............+478- suma Gauss cu formula de calcul S=[(n×(n+1)]:2
S=(478*479):2
S=114481

S = 1 + 2 + ...... 2000=(2000×2001):2=2001000-suma Gauss cu formula de calcul S=[(n×(n+1)]:2

S = 1 + 2 + 3 + ...... 170 =(170×171):2=14535-suma Gauss cu formula de calcul S=[(n×(n+1)]:2

B) 1 + 2 + 3 + ...... + 73 =(73×74):2=2701 -suma Gauss cu formula de calcul S=[(n×(n+1)]:2

S = 26 + 27 + ........ 175 progresie aritmetica
an=a1+(n-1)×r
an=175, a1=26
r=1
175=26+(n-1)×1
175-26+1=n
n=150
S=[(an+a1)×n]:2

S=(26+175)×150:2=15075