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\(\frac{\text{1984.1985 + 1986.20 + 1965}}{1985.200-1984.1986}=-1,123249617\approx-1,13\)
-\(\frac{1989.1985+1986.20+1965}{1985.2000-1984.1985}\)
\(=\frac{1989.1985+1986.20-20+1985}{1985\left(2000-1984\right)}\)
\(=\frac{1985\left(1989+20+1\right)}{1985.16}\)
\(=\frac{2010}{16}=\frac{1005}{8}=125,625\)
\(1984\cdot1985+1986\cdot20+\frac{1965}{1985\cdot2000}-1984\cdot1985\)
\(=3938240+39720+\frac{393}{794000}-3938240\)
\(=3938240-3938240+39720+\frac{393}{794000}\)
\(=39720+\frac{393}{794000}\)
\(=39720,00049\)rồi bạn tự đổi ra phân số nhé
ý câu hỏi là thế này mà bạn :
\(\frac{\text{1984.1985+1986.20+1965}}{\text{1985.2000-1984.1985}}\)
Bài 1:
A = \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)
= \(1-\frac{1}{50}=\frac{49}{50}\)
Bài 2:
Ta có: \(\frac{1}{1^2}=1;\frac{1}{2^2}< \frac{1}{1.2};\frac{1}{3^2}< \frac{1}{2.3};...;\frac{1}{50^2}< \frac{1}{49.50}\)
\(\Rightarrow A< 1+\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)
\(A< 1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}=1+1-\frac{1}{50}=2-\frac{1}{50}< 2\)
Vậy A < 2
Bài 3:
\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)
\(=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
\(=\frac{1}{5}-\frac{1}{12}=\frac{7}{60}\)
Bài 4:
\(S=3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\)
\(2S=6+3+\frac{3}{2}+...+\frac{3}{2^8}\)
\(2S-S=\left(6+3+\frac{3}{2}+...+\frac{3}{2^8}\right)-\left(3+\frac{3}{2}+\frac{3}{2^2}+...+\frac{3}{2^9}\right)\)
\(S=6-\frac{3}{2^9}=6-\frac{3}{512}=\frac{3069}{512}\)
A=1-1/2+1/2-1/3+.............................1/49-1/50
A=1-1/50
A=49/50
a.\(\frac{2001.2002-1}{400.2002+4002}\)
\(=\frac{2000}{4000+4002}\)
\(=\frac{2000}{8002}=\frac{1000}{4001}\)
b.\(\frac{1999.2000-1}{1998.1999+3997}\)
\(=\frac{2000-1}{1998+3997}\)
\(=\frac{1999}{5995}\)
a) \(\frac{2001.2002-1}{2001.2002-1+1999.2002+4003}=\frac{2001.2002-1}{\left(2001.2002-1\right)+1999.2002+4004-1}\)
\(=\frac{2001.2002-1}{\left(2001.2002-1\right)+2002.\left(1999+2\right)-1}\)
\(=\frac{2001.2002-1}{\left(2001.2002-1\right)+2002.2001-1}=\frac{1.\left(2001.2002-1\right)}{\left(2001.2002-1\right).2}\)
= 1/2
b) \(\frac{1999.2000-1}{1998.1999+3997}=\frac{1999.2000-1}{1998.1999+3998-1}\)
\(=\frac{1999.2000-1}{1999.\left(1998+2\right)-1}=\frac{1999.2000-1}{1999.2000-1}=1\)
\(2012+\frac{2012}{1+2}+\frac{2012}{1+2+3}+.....+\frac{2012}{1+2+3+....+2011}\)
\(=\frac{2012}{\frac{1\left(1+1\right)}{2}}+\frac{2012}{\frac{2\left(2+1\right)}{2}}+\frac{2012}{\frac{3\left(3+1\right)}{2}}+.....+\frac{2012}{\frac{2011\left(2011+1\right)}{2}}\)
\(=\frac{4024}{1.2}+\frac{4024}{2.3}+\frac{4024}{3.4}+.....+\frac{4024}{2011.2012}\)
\(=4024\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2011}-\frac{1}{2012}\right)\)
\(=4024\left(1-\frac{1}{2012}\right)\)
\(=4024.\frac{2011}{2012}\)
\(=4022\)
Mk biết làm ý a thôi
Rút gọn đi ta được: \(\frac{76}{67}-\frac{205}{302}\) rồi bạn tự tính nhá