Question

S=317+318+319+...400
URGENT !! DAU COROANA!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

Notam:

cu S₁ suma ceruta, adica S₁ = 317+318+319+...400

cu S₂   suma de la 1 la 316 , adica S₂ = 1+2+3+...+316

si cu  St suma totala de la 1 la 400 , adica St = 1+2+3+....+400

Aplicam suma lui Gauss :

St = 400*401/2=80200

S₂ = 316*317/2=50086

S₁ = St -S₂

S₁ = 80200 - 50086

S₁ = 30114

Succes !!

Answer 2

Metoda I:

S = 317+318+319+...+400

= 1+2+3+...+400 - (1+2+3+...+316)

= (400·401)/2 - (316·317)/2

= 200·401 - 158·317

= 30114

Metoda II:

S = 317+318+319+...+400

= (317+400)+(318+399)+(319+398)+...+(358+359)

= 717+717+717+...+717 {de 42 ori}

= 717×42

= 30114

Metoda III:

S = 317+318+319+...+400

= (316+1)+(316+2)+(316+3)+...+(316+84)

= 316×84 + 1+2+3+...+84

= 316×84 + (84×85)/2

= 316×84 + 42×85

= 30114