Question

S1=1+3 +5.... +2019=




S2=2+4+8+....+2020​

Answer 1

Răspuns:

Explicație pas cu pas:

S₁ = 1+3+5+7+....+2019

S₁ = (1+2019)·[(2019-1):2+1]:2

S₁ = 2020·1010:2 = 1010·1010 = 1010²

S₁ = 1020100

S₂ = 2+4+6+8+....+2020

S₂ = 2·(1+2+3+4+....+1010)

S₂ = 2·(1+1010)·1010:2

S₂ = 1011·1010 = >

S₂ = 1021110

Am folosit suma lui Gauss :

Sₙ = (a₁+aₙ)·n:2  ; n = numarul de termeni

n = (aₙ-a₁):r + 1 ;  r = ratia = a₂-a₁