Question

Am putin nevoie de ajutor la un ex. Multumesc :) ​

Answer 1

Răspuns:

Explicație pas cu pas:

Am putin nevoie de ajutor la un ex. ​

A=(1/2)·(3/4)·(5/6)·(7/8)·(9/10)·(11/12)·(13/14)·(15/16)·(17/18)·(19/20)

B=(2/3)·(4/5)·(6/7)·(8/9)·(10/11)·(12/13)·(14/15)·(16/17)·(18/19)·(20/21)

A·B=[(1/2)·(3/4)·(5/6)·(7/8)·(9/10)·(11/12)·(13/14)·(15/16)·(17/18)·(19/20)]·[(2/3)·(4/5)·(6/7)·(8/9)·(10/11)·(12/13)·(14/15)·(16/17)·(18/19)·(20/21)]=

(1/2)·(2/3)·(3/4)·(4/5)·(5/6)·(6/7)·(7/8)·(8/9)·(9/10)·(10/11)·(11/12)·(12/13)·(13/14)·(14/15)·(15/16)·(16/17)·(17/18)·(18/19)·(19/20)·(20/21)

La inmultire, am intercalat primul termen de la A cu primul termen de la B, al 2 lea termen de la A cu al 2 lea termen de la B, .....pana le-am scris pe toate. Dupa cum se poate vedea, se poate face simplificarea, 2 de la numitor cu 2 de la numarator fractia urmatoare. Acest lucru se repeta la toate fractiile.  ⇒Se simplifica toti termenii pari si raman cei impari.

Apoi simplificam termenii impari in mod asemanator.

A·B=(1/2)·(2/3)·(3/4)·(4/5)·(5/6)·(6/7)·(7/8)·(8/9)·(9/10)·(10/11)·(11/12)·(12/13)·(13/14)·(14/15)·(15/16)·(16/17)·(17/18)·(18/19)·(19/20)·(20/21)= (1/3)·(3/5)·(5/7)·(7/9)·(9/11)·(11/13)·(13/15)·(15/17)·(17/19)·(19/21)=

(1/5)·(5/7)·(7/9)·(9/11)·(11/13)·(13/15)·(15/17)·(17/19)·(19/21)=

(1/7)·(7/9)·(9/11)·(11/13)·(13/15)·(15/17)·(17/19)·(19/21)=

(1/9)·(9/11)·(11/13)·(13/15)·(15/17)·(17/19)·(19/21)=

(1/11)·(11/13)·(13/15)·(15/17)·(17/19)·(19/21)=

(1/13)·(13/15)·(15/17)·(17/19)·(19/21)=

(1/15)·(15/17)·(17/19)·(19/21)=

(1/17)·(17/19)·(19/21)=

(1/19)·(19/21)=

(1/21)  

⇒A·B=1/21

A trebuit sa scriu mai mult pentru a se putea vedea cum au fost facute simplificarile.:) ​