Đặt A=\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2005.2006}\)
B=\(\frac{1}{1004.2006}+\frac{1}{1005.2006}+...+\frac{1}{2006.1004}\)
Chứng tỏ rằng \(\frac{A}{B}\in Z\)
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Những câu hỏi liên quan
\(A=\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{2005.2006}\);\(B=\frac{1}{1004.2006}+\frac{1}{1005.2006}+...+\frac{1}{2006.1004}\)
Chứng minh rằng \(\frac{A}{B}\)thuộc Z
Đặt A=1/1.2+1/3.4+...+1/2005.2006,B=1/1004.2006+1/1005.2006+...+1/2006.1004 Chứng minh rằng A/B thuộc Z
Cho A=\(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{2005.2006}\)
B=\(\frac{1}{1004.2006}+\frac{1}{1005.2006}+\frac{1}{1006.2006}+...+\frac{1}{2006.2006}\)
Tính A chia B
Cho \(A=\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{1004.2006}\)
\(B=\frac{1}{1004.2006}+\frac{1}{1005.2006}+...+\frac{1}{2006.1004}\)
Tính \(\frac{A}{B}\)
Cho \(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+............+\frac{1}{2005.2006}\)
\(B=\frac{1}{1004.2006}+\frac{1}{1005.2005}+.....+\frac{1}{2006.1004}\)
Tính \(\frac{A}{B}\)
\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{2005.2006}\)
\(=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}\)
\(=\left(1+\frac{1}{3}+...+\frac{1}{2005}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2006}\right)\)
\(=\left(1+\frac{1}{2}+...+\frac{1}{2006}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2006}\right)\)
\(=\left(1+\frac{1}{2}+...+\frac{1}{2006}\right)-\left(1+\frac{1}{2}+...+\frac{1}{1003}\right)\)
\(=\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}\)(1)
\(B=\frac{1}{1004.2006}+\frac{1}{1005.2005}+....+\frac{1}{2006.1004}\)
\(\Rightarrow\frac{1}{1004}+\frac{1}{2006}+\frac{1}{1005}+\frac{1}{2005}+...+\frac{1}{2006}+\frac{1}{1004}=2\left(\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}\right)\)
\(=\frac{\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}}{1505}\)(2)
Thế (1) và (2) vào ta có:
\(\frac{A}{B}=\frac{\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}}{\frac{\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}}{1505}}\)
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Cho
\(A=\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{2003.2004}+\frac{1}{2005.2006}\)
\(B=\frac{1}{1004.2006}+\frac{1}{1005.2005}+\frac{1}{1006.2004}+...+\frac{1}{2006.1004}\)
Tìm \(\frac{A}{B}\)
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\(A=\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{2003.2004}+\frac{1}{2005.2006}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005}-\frac{1}{2006}\)\(=\left(1+\frac{1}{3}+...+\frac{1}{2005}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2006}\right)\)
\(=\left(1+\frac{1}{2}+...+\frac{1}{2006}\right)-2\cdot\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2006}\right)\)\(=\left(1+\frac{1}{2}+...+\frac{1}{2006}\right)-\left(1+\frac{1}{2}+...+\frac{1}{1003}\right)=\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}\)
\(B=\frac{1}{1004.2006}+\frac{1}{1005.2005}+\frac{1}{1006.2004}+...+\frac{1}{2006.1004}\)
=>3010B=\(\frac{1}{1004}+\frac{1}{2006}+\frac{1}{1005}+\frac{1}{2005}+...+\frac{1}{2006}+\frac{1}{1004}=2\cdot\left(\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}\right)\)
=>B=\(\frac{\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}}{1505}\)
=>\(\frac{A}{B}=\frac{\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}}{\frac{\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}}{1505}}=1505\)
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Cho:
\(A=\frac{1}{1.2}+\frac{1}{3.4}+.....+\frac{1}{2003.2004}+\frac{1}{2005.2006}\)
\(B=\frac{1}{1004.2006}+\frac{1}{1005.2005}+\frac{1}{1006.2004}+.....+\frac{1}{2006.1004}\)
Hãy tính \(\frac{A}{B}\)
1, Cho
A = \(\frac{1}{1.2}+\frac{1}{3.4}+....+\frac{1}{2005.2006}\)
B = \(\frac{1}{1004.2006}+\frac{1}{1005.2005}+\frac{1}{1006.2004}+.......+\frac{1}{2006.1004}\)
Hãy Tính \(\frac{A}{B}\)
A=1−12+13−14+...+12005−12006=(1+12+...+12006)−(1+12+..+11003)=11004+11005+...+12006" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.06px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:41.489em; padding:1px 0px; position:relative; white-space:nowrap; width:749.281px; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">
13010.B=11004+12006+11005+12005+...+11004=11505(11004+11005+...+12006)" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:18.06px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">
Suy ra A/B = 1505
Tham khảo nha
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\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2005.2006}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{2005}-\frac{1}{2006}\)
\(=1-\frac{1}{2006}\)
\(=\frac{2005}{2006}\)
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A=1/1.2+1/3.4+...+1/2005.2006 và B=1/1004.2006+1/1005.2006+...+1/2006.1004
CMR A/B thuộc Z
\(A=\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{2005.2006}\)
\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2005.2006}\)
\(A=\left(1+\frac{1}{3}+...+\frac{1}{2005}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2006}\right)\)
\(A=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2005}+\frac{1}{2006}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2006}\right)\)
\(A=\left(1+\frac{1}{2}+...+\frac{1}{2006}\right)-\left(1+\frac{1}{2}+...+\frac{1}{1003}\right)\)
\(A=\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}\)
\(B=\frac{1}{1004.2006}+\frac{1}{1005.2006}+...+\frac{1}{2006.1004}\)
\(3010B=\frac{1004+2006}{1004.2006}+\frac{1005+2005}{1005.2005}+...+\frac{2006+1004}{2006.1004}\) ( sửa đề nhé )
\(3010B=\frac{1}{2006}+\frac{1}{1004}+\frac{1}{2005}+\frac{1}{1005}+...+\frac{1}{1004}+\frac{1}{2006}\)
\(3010B=2\left(\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}\right)\)
\(B=\frac{\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}}{1505}\)
\(\Rightarrow\)\(\frac{A}{B}=\frac{\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}}{\frac{\frac{1}{1004}+\frac{1}{1005}+...+\frac{1}{2006}}{1505}}=1505\) hay \(\frac{A}{B}\inℤ\)
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