\(\frac{1995.1994-1}{1993.1995+1994}\)
K
Khách
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15 tháng 7 2020
Trả lời:
\(\frac{1995\times1994-1}{1993\times1995+1994}=\frac{1995\times\left(1993+1\right)-1}{1993\times1995+1994}\)
\(=\frac{1993\times1995+1995-1}{1993\times1995+1994}\)
\(=\frac{1993\times1995+1994}{1993\times1995+1994}\)
\(=1\)
13 tháng 8 2017
$a)\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{90}$
$=\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{9.10}$
$=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}$
$=\dfrac{1}{2}-\dfrac{1}{10}=\dfrac{2}{5}$
13 tháng 8 2017
b) Đặt $B=\dfrac{4}{2.4}+\dfrac{4}{4.6}+...+\dfrac{4}{18.20}$
$=>\dfrac{1}{2}B=\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{18.20}$
$=>\dfrac{1}{2}B=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{18}-\dfrac{1}{20}$
$=>\dfrac{1}{2}B=\dfrac{1}{2}-\dfrac{1}{20}=\dfrac{9}{20}$
$=>B=\dfrac{9}{10}$
c) $\dfrac{2}{3}+\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}$
$=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}$
$=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}$
$=1-\dfrac{1}{9}=\dfrac{8}{9}$
d) Viết lại đề rõ ràng nha bạn.
4 tháng 7 2017
\(A=\dfrac{1995.1994-1}{1993.1995+1994}=\dfrac{1995\left(1993+1\right)-1}{1993.1995+1994}=\dfrac{1995.1993+1995-1}{1993.1995+1994}=\dfrac{1995.1993+1994}{1995.1993-1994}=1\)\(B=\dfrac{2004.2004+3006}{2005.2005-1003}=\dfrac{2004.2004+2004.1+1002}{2005.2005-1003}=\dfrac{2004.2005+1002}{2005.2005-1003}=\dfrac{2004.2005+1002}{2004.2005+2005-1003}=\dfrac{2004.2005+1002}{2004.2005+1002}=1\)\(C=\dfrac{2010.2011-1}{2009.2011+2010}=\dfrac{2009.2011+2011-1}{2009.2011+2010}=\dfrac{2019.2011+2010}{2009.20011+2010}=1\)\(D=\dfrac{2014.2015-1}{2013.2015+2013}=\dfrac{2013.2015+2014-1}{2013.2015+2013}=\dfrac{2013.2015+2013}{2013.2015+2013}=1\)
LG
4 tháng 7 2017
Câu 1 nhầm đề nha bạn mình sửa:
\(\dfrac{1995.1994-1}{1993.1995+1994}\)
\(=\dfrac{1995.\left(1993+1\right)-1}{1993.1995+1994}\)
\(=\dfrac{1995.1993+1995-1}{1993.1995+1994}\)
\(=\dfrac{1993.1995+1994}{1993.1995+1994}\)
\(=1\)
Câu 2: \(\dfrac{2004.2004+3006}{2005.2005-1003}\)
\(=\dfrac{2004.2004+2004+1002}{\left(2004+1\right).\left(2004+1\right)-1003}\)
\(=\dfrac{2004.2004+2004+1002}{2004.2004+2004+1-1003}\)
\(=\dfrac{2004.2004+2004+1002}{2004.2004+2004+1002}\)
\(=1\)
Câu 3:\(\dfrac{2010.2011-1}{2009.2011+2010}\)
\(=\dfrac{\left(2009+1\right).2011-1}{2009.2011+2010}\)
\(=\dfrac{2009.2011+2011-1}{2009.2011+2010}\)
\(=\dfrac{2009.2011+2010}{2009.2011+2010}\)
= 1
Câu 4:Nhầm để, sửa:
\(\dfrac{2014.2015-1}{2013.2015+2014}\)
\(=\dfrac{\left(2013+1\right).2015-1}{2013.2015+2014}\)
\(=\dfrac{2013.2015+2015-1}{2013.2015+2014}\)
\(=\dfrac{2013.2015+2014}{2013.2015+2014}\)
\(=1\)
XO
12 tháng 7 2019
A = \(\frac{1995.1996-1997}{1995.1994+1993}\)
= \(\frac{1995.\left(1994+2\right)-1997}{1995.1994+1993}\)
= \(\frac{1995.1994+1995.2-1997}{1995.1994+1993}\)
= \(\frac{1995.1994+3990-1997}{1995.1994+1993}\)
= \(\frac{1995.1994+1993}{1995.1994+1993}\)
= \(1\)
b) B = \(\frac{12345.67890-54321}{12344.67890+13569}\)
= \(\frac{\left(12344+1\right).67890-54321}{12344.67890+13569}\)
= \(\frac{12344.67890+67890-54321}{12344.67890+13569}\)
= \(\frac{12344.67890+13569}{12344.67890+13569}\)
= \(1\)
N
11 tháng 11 2018
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a^{1994}}{b^{1994}}=\frac{c^{1994}}{d^{1994}}\)
áp dụng t/c dãy tỉ số bằng nhau ta có:
\(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}\)
\(\frac{a^{1994}}{b^{1994}}=\frac{\left(a+c\right)^{1994}}{\left(b+d\right)^{1994}}\)(1)
\(\frac{a^{1994}}{b^{1994}}=\frac{c^{1994}}{d^{1994}}=\frac{a^{1994}+c^{1994}}{b^{1994}+d^{1994}}\)(2)
từ (1) và (2) => \(\frac{a^{1994}+c^{1994}}{b^{1994}+d^{1994}}=\frac{\left(a+c\right)^{1994}}{\left(b+d\right)^{1994}}\left(đpcm\right)\)
\(\)
12 tháng 10 2015
\(\frac{a}{b}=\frac{c}{d}\)=\(\frac{a+c}{b+d}\)
=> \(\frac{a^{1994}}{b^{1994}}=\frac{c^{1994}}{d^{1994}}\)\(=\frac{\left(a+c\right)^{1994}}{\left(b+d\right)^{1994}}\)
=> \(\frac{a^{1994}+c^{1994}}{b^{1994}+d^{1994}}=\frac{\left(a+c\right)^{1994}}{\left(b+d\right)^{1994}}\)
=> dpcm
HT
1 tháng 10 2015
\(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}\)(Tính chất dãy tỉ số bằng nhau)
=> \(\frac{a^{1994}}{b^{1994}}=\frac{c^{1994}}{d^{1994}}=\frac{\left(a+c\right)^{1994}}{\left(b+d\right)^{1994}}=\frac{a^{1994}+c^{1994}}{b^{1994}+d^{1994}}\)(Tính chất dãy tỉ số bằng nhau)
=> \(\frac{\left(a+c\right)^{1994}}{\left(b+d\right)^{1994}}=\frac{a^{1994}+c^{1994}}{b^{1994}+d^{1994}}\)
=> Đpcm
Câu 2 tớ đăng phía dưới rồi đó.
Câu 3 đang định đăng lên thì cậu đăng là sao hả?
DT
1
21 tháng 7 2017
\(A=\frac{1995\cdot1996-1997}{1995\cdot1994+1993}\)
\(A=\frac{1995\cdot\left(1994+2\right)-1997}{1995\cdot1994+1993}\)
\(A=\frac{1995\cdot1994+1995\cdot2-1997}{1995\cdot1994+1993}\)
\(A=\frac{1995\cdot1994+3990-1997}{1995\cdot1994+1993}\)
\(A=\frac{1995\cdot1994+1993}{1995\cdot1994+1993}\)
\(A=1\)