Tìm x 1/3 + 1/6 +1/10 +…+2/x.(x+1)=2001/2003 27/09/2021 Bởi Katherine Tìm x 1/3 + 1/6 +1/10 +…+2/x.(x+1)=2001/2003
Đáp án: x=2002 Giải thích các bước giải: ta có $\frac{2}{x(x+1)}=2.(\frac{1}{x}-\frac{1}{x+1})$ $=>\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+…+\frac{2}{x(x+1)}=\frac{2001}{2003}$ $=>\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+…+\frac{2}{x(x+1)}=\frac{2001}{2003}$ $=>2.(\frac{1}{2}-\frac{1}{3})+2.(\frac{1}{3}-\frac{1}{4})+…+2.(\frac{1}{x}-\frac{1}{x+1})=\frac{2001}{2003}$ $=> 2(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+…+\frac{1}{x}-\frac{1}{x+1}=\frac{2001}{2003})$ $=> 2(\frac{1}{2}-\frac{1}{x+1})=\frac{2001}{2003}$ $=>\frac{x-1}{x+1}=\frac{2001}{2003}$ $=> x=2002$ Bình luận
Đáp án: x=2002 Giải thích các bước giải: VT= 2/6+2/12+2/20+….+2/ (x.(x+1)) =2/(2.3) +2/(3.4) +2/(4.5) +….+2/x.(x+1) =2.[ 1/(2.3) +1/(3.4) +1/(4.5)+….+ 1/x.(x+1)] =2.[ 1/2 – 1/3 + 1/3 -1/4 +1/4 – 1/5 +….+ 1/x – 1/(x+1)] = 2. [ 1/2- 1/(x+1)] = (x-1)/(x+1) = 2001/2003 vậy x= 2002 Bình luận
Đáp án:
x=2002
Giải thích các bước giải:
ta có $\frac{2}{x(x+1)}=2.(\frac{1}{x}-\frac{1}{x+1})$
$=>\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+…+\frac{2}{x(x+1)}=\frac{2001}{2003}$
$=>\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+…+\frac{2}{x(x+1)}=\frac{2001}{2003}$
$=>2.(\frac{1}{2}-\frac{1}{3})+2.(\frac{1}{3}-\frac{1}{4})+…+2.(\frac{1}{x}-\frac{1}{x+1})=\frac{2001}{2003}$
$=> 2(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+…+\frac{1}{x}-\frac{1}{x+1}=\frac{2001}{2003})$
$=> 2(\frac{1}{2}-\frac{1}{x+1})=\frac{2001}{2003}$
$=>\frac{x-1}{x+1}=\frac{2001}{2003}$
$=> x=2002$
Đáp án: x=2002
Giải thích các bước giải:
VT= 2/6+2/12+2/20+….+2/ (x.(x+1))
=2/(2.3) +2/(3.4) +2/(4.5) +….+2/x.(x+1)
=2.[ 1/(2.3) +1/(3.4) +1/(4.5)+….+ 1/x.(x+1)]
=2.[ 1/2 – 1/3 + 1/3 -1/4 +1/4 – 1/5 +….+ 1/x – 1/(x+1)]
= 2. [ 1/2- 1/(x+1)]
= (x-1)/(x+1) = 2001/2003
vậy x= 2002