Question

Determinați n pentru care 1/6+1/12+1/20+1/30+1/42+...+1/n(n+1)=0,41(6)
va rog ajutor!!

Answer 1

1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
........................
1/n(n+1)=1/n-1/(n+1)
adunam
1/2-1/(n+1)=0,41(6)

(n+1-2)/2(n+1)=(416-41)/900

(n-1)/2
(n-1)/2(n+1)=375/900=15/36=5/12

12(n-1)=5*2*(n+1)
12n-12=10n+10
2n=22
n=11

Answer 2

1/2·3+1/3·4+1/4·5+1/5·6+1/6·7+........+1/n(n+1)=0,41(6)
1/2-1/3+1/4-1/3+1/5-1/4+1/6-1/5+1/7-1/6+.......+1/n-1/(n+1)=(416-41)/900
1/2+1/n= 375/900
1/2-1/(n+1)=5/12
6/12-5/12=1/(n+1)
1/12=1/(n+1) ⇒n+1=12 ⇒n=11