Question

Cum rezolvam: 2+4+6+8+.....+3880-1-3-5-7-9-.....-1430​

Answer 1

Răspuns:

Explicație pas cu pas:

St  2+4+6+8+.....+3880-1-3-5-7-9-.....-1431 =

St = 2 ( 1+2+3+4+...1940) - ( 1+3+5+7+9+...1431)

S₁ = 1+2+3+4+...1940

S₁ = n*(n+1)/2

S₁ = 1940*1941/2

S₁ =1.882.770

S₂ =  1+3+5+7+9+...1431

S₂ = n*n             unde 2n-1 = 1431  si n=716

S₂ = 716*716

S₂ =512.656

St = 2*S₁ - S₂

St = 2 * 1.882.770 - 512.656

St =3.252.884

Succes !!