Question

Calculati: 1/23+2/23+3/23+....+22/23​

Answer 1

Răspuns:

1/23+2/23+3/23+....+22/23​ = 11

Explicație pas cu pas:

1/23+2/23+3/23+....+22/23​ = ?

1/23+2/23+3/23+....+22/23​ = (1+2+3+....+22)/23 =

FOLOSIM FORMULA LUI GAUSS =>

= [(1+22)·22:2]/23 = 23·11/23 = 11

1/23+2/23+3/23+....+22/23​ = 11

Answer 2

1/23+2/23+...+22/23=

(1+2+...+22)/23 (Acelasi numitor)

1+2+...+22 = (22*23)/2 = 11*23 (Suma lui Gauss)

(11*23)/23 = 11