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

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

TRẢ LỜI

1. 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))=3980/1991
=>2/1.2+2/2.3+2/3.4+…+2/(x.(x+1))=3980/1991
=>2(1/1.2+1/2.3+1/3.4+…+1/(x.(x+1))=3980/1991
=>2(1-1/2+1/2-1/3+1/3-1/4+…+1/x-1/(x+1))=3980/1991
=>2(1-1/(x+1))=3980/1991
=>1-1/(x+1)=3980/1991:2
=>1-1/(x+1)=3980/1991. 1/2
=>1-1/(x+1)=1990/1991
=>1/(x+1)=1-1990/1991
=>1/(x+1)=1991/1991-1990/1991
=>1/(x+1)=1/1991
=>x+1=1991
=>x=1991-1
=>x=1990

Trả lời
2. minhtuquynh
Giải đáp:
$\\$
1 + 1/3 + 1/6 + 1/10 + … +2/(x (x + 1) ) = 1 1989/1991
↔ 2/2 + 2/6 + 2/12 + 2/20 + … + 2/(x (x + 1) ) = 3980/1991
↔ 2 × [1/2 + 1/6 +  … + 1/(x (x+1) )] = 3980/1991
↔ 2 × [1/(1×2) + 1/(2×3) +  … + 1/(x (x+1) )] = 3980/1991
↔ 2 × [1 – 1/2 + 1/2 – 1/3 + … + 1/x – 1/(x+1)] = 3980/1991
↔ 2 × [1 + (- 1/2 + 1/2 – 1/3 + … + 1/x) – 1/(x+1)] = 3980/1991
↔ 2 × [1 – 1/(x+1)] = 3980/1991
↔ 1 – 1/(x+1) = 3980/1991 ÷ 2
↔ 1 – 1/(x+1) = 3980/1991 × 1/2
↔ 1 – 1/(x+1) = 1990/1991
↔ 1/(x+1) =1-1990/1991
↔1/(x+1)=1991/1991 – 1990/1991
↔1/(x+1) = 1/1991
↔ x+1=1991
↔x=1991-1
↔x=1990
Vậy x=1990

Trả lời