Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
ta có
A=\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}=\frac{1}{3}-\frac{1}{21}=\frac{2}{7}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{19.21}\)
\(=2\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{21}\right)\)
=\(\frac{4}{7}\)
\(\frac{\left(\frac{3}{15}+\frac{1}{4}+\frac{7}{20}\right)\times\frac{17}{49}}{5\frac{1}{3}+\frac{2}{5}}\)
\(=\frac{\left(\frac{12}{60}+\frac{15}{60}+\frac{21}{60}\right)\times\frac{17}{49}}{\frac{16}{3}\times\frac{2}{5}}\)
\(=\frac{\frac{48}{60}\times\frac{17}{49}}{\frac{80}{15}+\frac{6}{15}}\)
\(=\frac{\frac{816}{2940}}{\frac{86}{15}}\)
\(=\frac{816}{2940}:\frac{86}{15}\)
\(=\frac{816}{2940}\times\frac{15}{86}\)
\(=\frac{68}{245}\times\frac{15}{86}\)
\(=\frac{102}{2107}\)
2008=1+1+1+...+1 có 2008 số 1
1+(1+2007/2)+(1+2006/3)+...+(1+1/2008)=2009/2009+2009/2+2009/3+...+2009/2008
=2009*(1/2009+1/2+1/3+...+1/2008)=2009*(1/2+1/3+...+1/2009)
ta có 2008+2007/2+...+1/2008
1/2+1/3+..............+1/2009
=2009
2008 + 2007/2 + 2006/3 + 2005/4 + ... + 2/2007 + 1/2008
2009-1/1 + 2009-2/2 + 2009-3/3 + 2009-4/4 + ... + 2009-2007/2007 + 2009-2008/2008
2009 - 1 + 2009/2 - 1 + 2009/3 - 1 + 2009/4 - 1 + ... + 2009/2007 - 1 + 2009/2008 - 1
2009 + 2009.(1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 ) - ( 1 + 1 + 1 + 1 + ... + 1 + 1 )
2009 + 2009.( 1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 ) - 2008
1 + 2009.( 1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 )
2009.( 1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 + 1/2009 )
=> giá trị của biểu thức trên là 2009
a,11/5x3/2-3/1/2x3/5
=11/2x3/5-7/2-3/5
=3/5x(11/2-7/2)
=3/5x2
=6/5
b,(1/2-1/3+1/4-1/5):(1/4-1/6)
=(1/6+1/20):1/12
=13/60:1/2
=13/30
\(=1-\frac{1}{3}+\frac{2}{3.5}+...+\frac{2}{15.17}\)
\(=1-\frac{1}{3}+2.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{15.17}\right)\)
\(=1-\frac{1}{3}+2.\left(\frac{1}{3}-\frac{1}{17}\right)\)
\(=\frac{62}{51}\)
\(\Leftrightarrow A=1-\frac{1}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{13.15}+\frac{2}{15.17}\)
\(\Leftrightarrow A=\frac{2}{1.3}+\frac{2}{3.5}+......+\frac{2}{13.15}+\frac{2}{15.17}\)
\(\Leftrightarrow A=1-\frac{1}{17}=\frac{16}{17}\)