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a: \(2\dfrac{3}{5}+1\dfrac{2}{5}\cdot\dfrac{31}{2}\)
\(=\dfrac{13}{5}+\dfrac{7}{5}\cdot\dfrac{31}{2}\)
\(=\dfrac{26}{10}+\dfrac{217}{10}=\dfrac{243}{10}\)
b: \(4\dfrac{3}{4}-3\dfrac{2}{3}:1\dfrac{1}{6}\)
\(=\dfrac{19}{4}-\dfrac{11}{3}:\dfrac{7}{6}\)
\(=\dfrac{19}{4}-\dfrac{11}{3}\cdot\dfrac{6}{7}\)
\(=\dfrac{19}{4}-\dfrac{22}{7}\)
\(=\dfrac{19\cdot7-22\cdot4}{28}=\dfrac{45}{28}\)
a, 1727 + [ 6993 : 111 + ( 848 - 95 ) ] x 4 - 2
= 1727 + [ 63 + 753 ] x 4 - 2
= 1727 + 816 x 4 - 2
= 1727 + 3264 - 2
= 4991 - 2
= 4989
b, 75/100 + 18/21 + 19/32 + 1/4 + 3/21 + 13/32
= 75/100 + 1/4 + ( 18/21 + 3/21 ) + ( 19/32 + 13/32 )
= 75/100 + 25/100 + 21/21 + 32/32
= 100/100 + 1 + 1
= 1 + 1 + 1 = 3
c, 4 2/5 + 5 6/9 + 2 3/4 + 3/5 + 1/3 + 1/4
= ( 4 2/5 + 3/5 ) + ( 2 3/4 + 1/4 ) + 5 6/9 + 1/3
= 5 + 3 + 5 6/9 + 3/9
= 5 + 3 + 6
= 8 + 6 = 14
d, 3/4 + 25/36 - ( 4/9 + 13/18 + 1/72 )
= 27/36 + 25/36 - ( 32/72 + 52/72 + 1/72 )
= 52/36 - ( 84/72 + 1/72 )
= 52/36 - 85/72
= 104/72 - 85/72
= 19/72
a )
75/100 + 18/21 + 19/32 + 1/4 + 3/21 + 13/32
= 3/4 + 18/21 + 19/321 + 1/4 + 3/21 + 13/32
= ( 3/4 + 1/4 ) + ( 18/21 + 3/21 ) + ( 19/32 + 13/32 )
= 1 + 1 + 1
= 3
b )
4 và 2/5 + 5 và 6/9 + 2 và 3/4 + 1/4 + 1/3 + 3/5
= 22/5 + 51/9 + 11/4 + 1/4 + 1/3 + 3/5
= ( 22/5 + 3/5 ) + ( 51/9 + 1/3 ) + ( 11/4 + 1/4 )
= 25/5 + 54/9 + 12/4
= 5 + 6 + 3
= 14
a)\(\frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}=\frac{3}{4}+\frac{18}{21}+\frac{1}{4}+\frac{19}{32}+\frac{3}{21}+\frac{13}{32}\)
\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\left(\frac{18}{21}+\frac{3}{21}\right)+\left(\frac{19}{32}+\frac{13}{32}\right)\)
\(=1+1+1=3\)
\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{19\cdot20}\)
=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)(Dùng cộng rồi trừ chính số đó bằng 0)
=\(\frac{1}{2}-\frac{1}{20}\)
=\(\frac{10}{20}-\frac{1}{20}\)( Dùng phương pháp quy đồng)
=\(\frac{9}{20}\)
\(\frac{1}{2.2}< \frac{1}{1.2}\)
\(\frac{1}{3.3}< \frac{1}{2.3}\)
......
\(\frac{1}{100.100}< \frac{1}{99.100}\)
\(\Rightarrow\frac{1}{2.2}+\frac{1}{3.3}+...+\frac{1}{100.100}< \frac{1}{1.2}+..+\frac{1}{99.100}\)
\(\Rightarrow\frac{1}{2.2}+..+\frac{1}{100.100}< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}...+\frac{1}{99}-\frac{1}{100}\)
\(\Rightarrow\frac{1}{2.2}+..+\frac{1}{100.100}< 1-\frac{1}{100}< 1\).Suy ra điều phải chứng minh. câu b tương tự. bấm đúng cho mình nha
BÀI 1:
\(541-\left(125-x\right)\times2\frac{2}{3}=469\)
\(\Rightarrow541-\left(125-x\right)\times\frac{8}{3}=469\)
\(\Rightarrow541-\frac{1000}{3}+\frac{8}{3}\times x=469\)
\(\Rightarrow\frac{623}{3}-\frac{8}{3}\times x=469\)
\(\Rightarrow\frac{8}{3}\times x=\frac{784}{3}\)
\(\Rightarrow x=98\)
BÀI 2 :
\(A=\frac{1}{2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...\)\(+\frac{1}{18\times19\times20}\)
\(=\frac{1}{2}\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}\right)+\frac{1}{2}\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}\right)\)\(+...+\frac{1}{2}\times\left(\frac{1}{18\times19}+\frac{1}{19\times20}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{2\times3}+...+\frac{1}{19\times20}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{1\times2}-\frac{1}{19\times20}\right)\)
\(=\frac{1}{2}\times\frac{189}{380}\)
\(=\frac{189}{760}\)
ĐÃ ĐÁP ỨNG THỈNH CẦU
a: ( 1 - 1/2 ) * ( 1 - 1/3 ) * ( 1 - 1/4 ) * ... * ( 1 - 1/18 ) * ( 1 - 1/19 ) * ( 1 - 1/20 )
=1/2*2/3*3/4*....*18/19*19/20
=1/20
b: 1 và 1/2 * 1 và 1/3 * 1 và 1/4 * 1 và 1/5 * ...* 1 và 1/2005 * 1 và 1/2006 * 1 và 1/ 2007
=3/2*4/3*5/4*...*2007/2006*2008/2007
=2008/2=1004
Ta có :
\(A=\frac{1}{2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{18.19.20}\)
\(\Rightarrow A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{18.19.20}\)
\(\Rightarrow A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{18.19}-\frac{1}{19.20}\right)\)
\(\Rightarrow A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{19.20}\right)\)
\(\Rightarrow A=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{380}\right)\)
\(\Rightarrow A=\frac{1}{4}-\frac{1}{760}< \frac{1}{4}\)
Vậy \(A< \frac{1}{4}\)
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{18.19.20}\)
\(\Rightarrow A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{18.19}-\frac{1}{19.20}\right)\)
\(\Rightarrow A=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{380}\right)=\frac{1}{2}\left(\frac{189}{380}\right)=\frac{189}{760}< \frac{1}{4}\)