Tìm các số nguyên x thỏa mãn:
\(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+2\right):2}=1\frac{2009}{2011}\)
tìm x, y thỏa mãn
a, \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{1}{x.\left(x+2\right):2}=1\frac{2009}{2011}\)
Tìm x biết: \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2009}{2011}\)
Tìm x biết: \(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+2\right):2}=\)\(1\frac{2009}{2011}\)
\(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{\frac{x\left(x+2\right)}{2}}=1\frac{2009}{2011}\)
\(\Leftrightarrow1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{1}{x\left(x+2\right)}=1\frac{2009}{2011}\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+....+\frac{2}{x\left(x+2\right)}=1\frac{2009}{2011}-1\)
\(\Leftrightarrow\left[2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+2}\right)\right]=\frac{2009}{2011}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+2}\right)=\frac{2009}{2011}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+2}=\frac{2009}{2011}\div2=\frac{2009}{4022}\)
\(\Leftrightarrow\frac{1}{x+2}=\frac{1}{2}-\frac{2009}{4022}=\frac{1}{2011}\)
\(\Leftrightarrow x=2011-2=2009\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+1\right):2}=\frac{2009}{2011}\)
có \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+1\right):2}=\frac{2009}{2011}\)
tách vế trái đặt là A
ta lại có\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+1\right):2}\)
\(\frac{1}{2}A=\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{x.\left(x+1\right):2}\right)\)
\(\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+...+\frac{1}{x.\left(x+1\right)}\)
\(\frac{1}{2}A=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x.\left(x+1\right)}\)
\(\frac{1}{2}A=\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+...+\left(\frac{1}{x}-\frac{1}{x+1}\right)\)
\(\frac{1}{2}A=\frac{1}{2}-\frac{1}{x+1}\)
\(A=\left(\frac{1}{2}-\frac{1}{x+1}\right):\frac{1}{2}\)
\(A=1+\frac{1}{\left(x+1\right):2}\)
ta thế vào vế trái vào vế phải
ta có\(1+\frac{1}{\left(x+1\right):2}=\frac{2009}{2011}\)
\(\frac{1}{\left(x+1\right):2}=\frac{2009}{2011}-1\)
\(\frac{1}{\left(x+1\right):2}=\frac{2009}{2011}-\frac{2011}{2011}=-\frac{2}{2011}\)
\(-\frac{2}{-\left(x+1\right)}=-\frac{2}{2011}\)
thấy hai tử bằng nhau
\(\Rightarrow-\left(x+1\right)=2011\)
\(\Rightarrow\left(x+1\right)=-2011\)
\(\Rightarrow x=-2011-1=-2012\)
Cho 3 số x y z thỏa mãn x + y + z = 2010 và \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{2010}\)
Tính giá trị biểu thức P= \(\left(x^{2007}+y^{2007}\right)\left(y^{2009}+z^{2009}\right)\left(z^{2011}+x^{2011}\right)\)
Tìm x biết \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{2009}{2011}\)
2.[1/6+1/12+1/20+...+1/x.(x+1)]=2009/2011
2.[1/2.3+1/3.4+1/4.5+...+1/x(x+1)]=2009/2011
1/2-1/3+1/3-1/4+...+1/x-1/(x+1)=2009/4022
1/2-1/(x+1)=2009/4022
1/(x+1)=1/2001
x+1=2011
x=2010
\(=>\frac{2}{3.2}+\frac{2}{6.2}+\frac{2}{10.2}+...+\frac{2}{x.\left(x+1\right):2.2}=\frac{2009}{2011}\)
\(=>\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x.\left(x+1\right)}=\frac{2009}{2011}\)
\(=>2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{2009}{2011}\)
\(=>\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{2009}{2011}:2\)
\(=>1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2009}{4022}\)
\(=>1-\frac{1}{x+1}=\frac{2009}{4022}\)
\(=>\frac{1}{x+1}=1-\frac{2009}{4022}\)
\(=>\frac{1}{x+1}=\frac{2013}{4022}\)
\(=>\frac{2013}{2013.\left(x+1\right)}=\frac{2013}{4022}\)
=>2013.(x+1)=4022
=>x+1=4022/2013
=>x=4022/2013-1
=>x=2009/2013
tìm x biết: \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2009}{2011}\)
Giả sử x là số nguyên dương
\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2009}{2011}\)
\(\Leftrightarrow2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2009}{2011}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2009}{2011}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{4022}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2009}{4022}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2011}\)
\(\Leftrightarrow x+1=2011\)
\(\Rightarrow x=2010\)
Tìm tập hợp các số nguyên x thỏa mãn :
a) \(3\frac{1}{3}:2\frac{1}{2}-1
Tìm tập hợp các số nguyên x thỏa mãn:
a, \(3\frac{1}{3}:2\frac{1}{2}-1< x< 7\frac{2}{3}.\frac{3}{7}+\frac{5}{2}\)
b,\(\frac{1}{2}-\left(\frac{1}{3}+\frac{1}{4}\right)< x< \frac{1}{48}-\left(\frac{1}{16}-\frac{1}{6}\right)\)