Question

Rezolvați ecuația :

$x (1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ... + \frac{1}{2019} ) = 2019 - \frac{1}{2} - \frac{2}{3} - \frac{3}{4} - ... - \frac{2018}{2019}$

Repede! Vă rog! ​

Answer 1

Răspuns:

Explicație pas cu pas:

-1/2 = -1+1/2 ; -2/3 = -1+1/3 ; -3/4 = -1+1/4 ...

Partea dreapta:

S=2019+(-1-1-1...-1) +1/2+1/3+1/4+...+1/2019

S = 2019-2018 +1/2+1/3+1/4+...+1/2019

S = 1+1/2+1/3+1/4+...+1/2019

x*S = S

x = 1