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trả lới thứ nhất: Bài này nói vế số đối, không giải kiểu phương trình: X+...+1999=0=> x=-1999 "tạo thành 1999 cặp số đối"/%
[ X x 0,25 + 1999 ] x 2000 = [ 53 + 1999 ] x2000
\(\Rightarrow\)x=212
[ X x 0,25 + 1999 ] x 2000 = [ 53+1999 ] x 2000
[ X x 0,25 + 1999 ] = [ 53+1999 ] x 2000 : 2000
X x 0,25 + 1999 = 53+1999
X x 0,25 = 53 + 1999 - 1999
X x 0,25 = 53
X = 53 : 0,25 =212
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)}=\frac{1999}{2001}\)
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{1999}{2001}\)
\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{1999}{2001}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1999}{2001}:2=\frac{1999}{4002}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{1999}{4002}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{1999}{2001}=\frac{1}{2001}\)
=> x + 1 = 2001
=> x = 2001 - 1
=> x = 2000
\(\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+..+\frac{2}{x\left(x+1\right)}=\frac{1999}{2001}\)
\(2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+..+\frac{1}{x\left(x+1\right)}\right)=\frac{1999}{2001}\)
\(\frac{1}{6}+\frac{1}{12}+..+\frac{1}{x\left(x+1\right)}=\frac{1999}{2001}:\frac{1}{2}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{1999}{4002}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{x}-\frac{1}{x+1}=\frac{1999}{4002}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{1999}{4002}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{1999}{4002}\)
\(\frac{1}{x+1}=\frac{1}{2001}\)
=> x + 1 = 2001
=> x = 2001 - 1
=> x = 2000
a)(x.0,25+1999)x2000=(53+1999)x2000
(x.0,25+1999)=53+1999
x.0,25=53
x=53x4
x=210
a)(x.0,25+1999)x2000=(53+1999)x2000
(x.0,25+1999)=53+1999
x.0,25=53
x=53x4
x=210
k mik đi
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+..+\frac{2}{x\left(x+1\right)}=\frac{1999}{2001}\)
\(2\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+..+\frac{1}{x\left(x+1\right)}\right)=\frac{1999}{2001}\)
\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{1999}{2001}:2\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{x}-\frac{1}{x+1}=\frac{1999}{4002}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{1999}{4002}\)
\(\frac{x+1-2}{2\left(x+1\right)}=\frac{1999}{4002}\Rightarrow\frac{x-1}{2\left(x+1\right)}=\frac{1999}{4002}\Leftrightarrow4002\left(x-1\right)=1999.2\left(x+1\right)\)
=> 4002x - 4002 = 3998x + 3998
=> 4002x - 3998x = 3998 + 4002
=> 4x = 8000
=> x = 2000
!/3+1/6+1/10+...+2/x(x+1)=1999/2001
1/6+1/12+1/20+...+2/x(x+1)=1999/2001
2(1/6+1/12+1/20+...+1/x(x+1)=1999/2001
1/6+1/12+1/20+1/x(x+1)=1999/2001:2
1/6+1/12+1/20+...+1/x(x+1)=1999/4002
1/2x3+1/3x4+1/4x5+...+1/x(x+1)=1999/4002
1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=1999/4002
1/2-1/x+1=1999/4002
1/x+1=1/2-1999/4002
1/x+1=1/2001
=>x+1=2001
=>x=2001-1
=x=2000
Vậy x=2000.