cho hai biểu thức sau:
\(A=\frac{1}{2\times17}+\frac{1}{3\times18}+.............+\frac{1}{1990\times2005}\)
\(B=\frac{1}{2\times1991}+\frac{1}{3\times1992}+..................+\frac{1}{16\times2005}\)
Những câu hỏi liên quan
So sánh 2 phân số: \(A=\frac{2005\times2005+1}{2005\times2005\times2005-1};B=\frac{2005+1}{2005\times2005-1}\)
Ta làm đơn giản :
A = \(\frac{2005x2005+1}{2005x2005x2005-1}=\frac{1}{2005-1}=\frac{1}{2004}\)
B = \(\frac{2005+1}{2005x2005-1}\)=\(\frac{2006}{4020024}=\frac{1}{2004}\)
\(\frac{1}{2004}=\frac{1}{2004}\)
Nên A = B
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\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+............+\frac{2}{2004\times2005}\)
giúp mình nhé
\(a=\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+......+\frac{1}{2003\times2005}\)
a=1/3x5+1/5x7+...+1/2003x2005
a=1x2/3x5x2+1x2/5x7x2+...+1x2/2003x2005x2
a=1/2(2/3x5+2/5x7+...+2/2003x2005)
a=1/2x(1/3-1/5+1/5-1/7+...+1/2003-1/2005)
a=1/2x(1/3-1/2005)
a=1/2x2002/6015
a=1001/6015
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A = 1/3.5 + 1/5.7 + 1/7.9 + .... + 1/2003.2005
2A = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + .... + 1/2003 - 1/2005
2A = 1/3 - 1/2005 = 2002/6015
=>A = 1001/6015
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\(\frac{1}{2}A=\)\(2\times\left(\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+...+\frac{1}{2003\times2005}\right)\)
\(\Leftrightarrow\frac{1}{2}A=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{2003\times2005}\)
\(\Leftrightarrow\frac{1}{2}A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2003}-\frac{1}{2005}\)
\(\Leftrightarrow\frac{1}{2}A=\frac{1}{3}-\frac{1}{2005}\)
\(\Leftrightarrow\frac{1}{2}A=\frac{2002}{6015}\)
\(\Leftrightarrow A=\frac{1001}{6015}\)
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21 tháng 7 2018 lúc 10:28
Tính
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{2004\times2005}+\frac{1}{2005\times2006}=A\)
\(\frac{1}{6}+\frac{2}{15}+\frac{4}{45}+\frac{2}{99}+\frac{10}{600}=A\)
\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2004\cdot2005}+\frac{1}{2005\cdot2006}\)
\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2004}-\frac{1}{2005}+\frac{1}{2005}-\frac{1}{2006}\)
\(A=1-\frac{1}{2006}=\frac{2005}{2006}\)
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\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2005.2006}\)
\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2005}-\frac{1}{2006}\)
\(\Rightarrow A=1-\frac{1}{2006}\)
\(\Rightarrow A=\frac{2005}{2006}\)
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\(1)A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2004.2005}+\frac{1}{2005.2006}\)
\(\implies A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2004}-\frac{1}{2005}+\frac{1}{2005}-\frac{1}{2006}\)
\(\implies A=1-\frac{1}{2006}\)
\(\implies A=\frac{2005}{2006}\)
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Xem thêm câu trả lời
BÀI 1 : So sánh
A = \(\frac{17^{18}+1}{17^{19}+1}\)và B = \(\frac{17^{17}+1}{17^{18}+1}\) So sánh A và B
\(\frac{n}{n+3}\)và \(\frac{n+1}{n+2}\)
\(\frac{2003\times2004-1}{2003\times2004}\)và \(\frac{2004\times2005-1}{2004\times2005}\)
chứng minh rằng \(\frac{A}{B}\) là số nguyên
A = \(\frac{1}{1\times2}+\frac{1}{3\times4}+...+\frac{1}{2005\times2006}\)
B = \(\frac{1}{1004\times2006}+\frac{1}{1005\times2005}+...+\frac{1}{2006\times1004}\)
Tính hợp lí:
A=\(\frac{5}{12\times17}+\frac{35}{17\times18}-\frac{39}{18\times21}+\frac{30}{21\times72}\)
B=\(\frac{767676\times31-626262\times38}{1^2+2^3+3^4+......+99^{100}}\)
tính bằng cách hợp lí :
\(\frac{1}{2001\times2003}+\frac{1}{2003\times2005}+\frac{1}{2005\times2007}+.....+\frac{1}{2009\times2011}+\frac{1}{2011\times2013}\)
Ta có: 1/ 2001 . 2003 = 1/2001 - 1/2003...
=> 1/2001 - 1/2003 + 1/2003 - 1/2005 + 1/2005 - 1/2007 + ... +1/2009 - 1/2011 +1/2011 - 1/2013
= 1/2001 - 1/2013
= 4/ 1342671
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\(\frac{1}{2001\times2003}\)+\(\frac{1}{2003\times2005}\)+\(\frac{1}{2005\times2007}\)+........+\(\frac{1}{2009\times2011}\)+\(\frac{1}{2011\times2013}\)
=\(\frac{1}{2001}-\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2005}+\frac{1}{2005}-\frac{1}{2007}\)+........+\(\frac{1}{2009}\)-\(\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2013}\)
=\(\frac{1}{2001}\)-\(\frac{1}{2013}\)
=\(\frac{2013}{4028013}-\frac{2001}{4028013}\)=\(\frac{2}{4028013}\)
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Xem thêm câu trả lời
tính giá trị biểu thức: A=\(\frac{5}{12\times17}+\frac{35}{17\times18}-\frac{39}{18\times21}+\frac{30}{21\times72}\)