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222-9+11+12:2*14+14 = ? ( )

## Toán Lớp 6: 1+1/3+1/6+1/10+-…+2/Xx(X+1)=1-1989/1991

Toán Lớp 6: 1+1/3+1/6+1/10+…….+2/Xx(X+1)=1-1989/1991

1. Giải đáp:
x=1/1990
Lời giải và giải thích chi tiết:
1+1/3+1/6+1/10+…+2/(x(x+1))=1-1989/1991
=>1+1/3+1/6+1/10+…+1/(x(x+1):2)=2/1991
=>1/2+1/6+1/12+1/20+…+1/(x(x+1))=1/1991
=>1/1.2+1/2.3+1/3.4+1/4.5+…+1/(x(x+1))=1/1991
=>1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…+1/x-1/(x+1)=1/1991
=>1-1/(x+1)=1/1991
=>1/(x+1)=1-1/1991
=>1/(x+1)=1990/1991
=>x+1=1991/1990
=>x=1991/1990-1
=>x=1/1990
Vậy x=1/1990.

2. Giải đáp + Lời giải và giải thích chi tiết:
1+1/3+1/6+…+2/(x.(x+1))=1-1989/1991
=>2/2+2/6+2/12+…+2/(x.(x+1))=1991/1991-1989/1991
=>2/1.2+2/2.3+2/3.4+…+2/(x.(x+1))=2/1991
=>2(1/1.2+1/2.3+1/3.4+…+1/(x.(x+1))=2/1991
=>2(1-1/2+1/2-1/3+1/3-1/4+…+1/x-1/(x+1))=2/1991
=>2(1-1/(x+1))=2/1991
=>1-1/(x+1)=2/1991:2
=>1-1/(x+1)=2/1991. 1/2
=>1-1/(x+1)=1/1991
=>1/(x+1)=1-1/1991
=>1/(x+1)=1991/1991-1/1991
=>1/(x+1)=1990/1991
=>x+1=1991/1990
=>x=1991/1990-1
=>x=1991/1990-1990/1990
=>x=1/1990