Question

Dau coroana!URGENT!ex:18.

Answer 1

calcul direct
 membru drept
(1/k) *(n+k-n)/n(n+k)=(k/k)*(1/n(n+k))=1/n(n+k)

atunci
1/1*3=1/1*(1+2)=(1/2)(1/1-1/3)

1/3*5=1/3*(3+2)=1/2(1/3-1/5)
.................................................
1/89*91=1/89*(89+2) =1/2(1/89-1/91)
si
1/1*3+1/3*5+1/5*7+...+1/89*91=(1/2)*(1/1-1/3+1/3-1/5+...+1/89-1/91)=
(1/2)*(1/1-1/91)=(1/2)*(90/91)=45/91




b) analog
S=(1/4)*(1/1-1/5+1/5-1/9+1/9-1/13+...+1/81-1/85)=
(1/4)*(1/1-1/85)=(1/4)*(1/1-1/85)=(1/4) *(84/85)=21/85


c) analog
S=(1/4) (1/1*2+1/2*3+1/3*4+...+1/35*36) =
(1/4) *(1/1)* (1/1-1/2+1/2-1/3+1/3-1/4+...+1/35-1/36)=
(1/4)*(1-1/36) =(1/4) *(35/36)=35/144


d) analog
S= (1/3) (1/1-1/4+1/4-1/7+1/7-1/10+...+1/88-1/91)=
(1/3) (1/1-1/91)=(1/3) *(90/91)=30/91