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21 tháng 6 2023
1: =(-20/36+15/36)*(-3/10)+(-16/36+21/36)
=-5/36*(-3/10)+5/36
=5/36*13/10
=65/360=13/72
2: Bạn xem lại đề nha bạn, dãy số này không có quy luật nào hết luôn á
Q
9 tháng 4 2017
a) \(P=\dfrac{1}{1.2}+\dfrac{2}{2.4}+\dfrac{3}{4.7}+...\dfrac{10}{46.56}\)
\(P=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...\dfrac{1}{46}-\dfrac{1}{56}\)
\(P=1-\dfrac{1}{56}\)
\(P=\dfrac{55}{56}\)
b) \(A=\dfrac{3}{1.2}+\dfrac{3}{2.3}+\dfrac{3}{3.4}+...+\dfrac{3}{99.100}\)
\(A=3\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right)\)
\(A=3\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(A=3\left(1-\dfrac{1}{100}\right)\)
\(A=3.\dfrac{99}{100}\)
\(A=\dfrac{297}{100}\)
c) \(B=\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{100.103}\)
\(B=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{100}-\dfrac{1}{103}\)
\(B=1-\dfrac{1}{103}\)
\(B=\dfrac{102}{103}\)
d) \(C=\dfrac{5}{1.4}+\dfrac{5}{4.7}+\dfrac{5}{7.10}+...+\dfrac{5}{100.103}\)
\(C=\dfrac{5}{3}\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{100.103}\right)\)
\(C=\dfrac{5}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{100}-\dfrac{1}{103}\right)\)
\(C=\dfrac{5}{3}\left(1-\dfrac{1}{103}\right)\)
\(C=\dfrac{5}{3}.\dfrac{102}{103}\)
\(C=\dfrac{170}{103}\)
e) \(D=\dfrac{7}{1.5}+\dfrac{7}{5.9}+\dfrac{7}{9.13}+...+\dfrac{7}{101.105}\)
\(D=\dfrac{7}{4}\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+\dfrac{4}{9.13}+...+\dfrac{4}{101.105}\right)\)
\(D=\dfrac{7}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{101}-\dfrac{1}{105}\right)\)
\(D=\dfrac{7}{4}\left(1-\dfrac{1}{105}\right)\)
\(D=\dfrac{7}{4}.\dfrac{104}{105}\)
\(D=\dfrac{26}{15}\)
12 tháng 8 2019
những ai thích xem minecraft và blockman go thì hãy xem kênh youtube của mik kênh mik là M.ichibi các bn nhớ sud và chia sẻ cho nhiều người khác nhé
D
9 tháng 4 2017
a)\(P=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+...+\frac{1}{46}-\frac{1}{56}\)
=\(1-\frac{1}{56}=\frac{55}{56}\)
b)\(A.\frac{1}{3}=\frac{1}{3}.\left(\frac{3}{1.2}+\frac{3}{2.3}+....+\frac{3}{99.100}\right)\)
= \(\frac{1}{3}A=\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{3}{99.100}\)
=> \(\frac{1}{3}A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
=> \(\frac{1}{3}A=1-\frac{1}{100}=\frac{99}{100}\)
=> \(A=\frac{99}{100}.3=\frac{297}{100}\)
c)\(B=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{100}-\frac{1}{103}\)
=\(1-\frac{1}{103}=\frac{102}{103}\)
d) \(\frac{3}{5}C=\frac{3}{5}.\left(\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{100.103}\right)\)
=\(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{100.103}\)
=\(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+....+\frac{1}{100}-\frac{1}{103}\)
=\(1-\frac{1}{103}=\frac{102}{103}\)
=>\(C=\frac{102}{103}.\frac{5}{3}=\frac{170}{103}\)
e) \(\frac{4}{7}D=\frac{4}{7}.\left(\frac{7}{1.5}+\frac{7}{5.9}+...+\frac{7}{101.105}\right)\)
=\(\frac{4}{1.5}+\frac{4}{5.9}+...+\frac{4}{101.105}\)
=\(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{101}-\frac{1}{105}\)
=\(1-\frac{1}{105}=\frac{104}{105}\)
=< D=\(\frac{104}{105}.\frac{7}{4}=\frac{26}{15}\)
D
0
MV
14 tháng 5 2017
B1
a)
\(\dfrac{1}{1\cdot4}+\dfrac{1}{4\cdot7}+\dfrac{1}{7\cdot10}+...+\dfrac{1}{28\cdot31}\\
=\dfrac{1}{3}\cdot\dfrac{3}{1\cdot4}+\dfrac{1}{3}\cdot\dfrac{3}{4\cdot7}+\dfrac{1}{3}\cdot\dfrac{3}{7\cdot10}+...+\dfrac{1}{3}\cdot\dfrac{3}{28\cdot31}\\
=\dfrac{1}{3}\cdot\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+...+\dfrac{3}{28\cdot31}\right)\\
=\dfrac{1}{3}\cdot\left(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{28}-\dfrac{1}{31}\right)\\
=\dfrac{1}{3}\cdot\left(1-\dfrac{1}{31}\right)\\
=\dfrac{1}{3}\cdot\dfrac{30}{31}\\
=\dfrac{10}{31}\)
b)
\(\dfrac{5}{1\cdot3}+\dfrac{5}{3\cdot5}+\dfrac{5}{5\cdot7}+...+\dfrac{5}{99\cdot101}\\
=\dfrac{5}{2}\cdot\dfrac{2}{1\cdot3}+\dfrac{5}{2}\cdot\dfrac{2}{3\cdot5}+\dfrac{5}{2}\cdot\dfrac{2}{5\cdot7}+...+\dfrac{5}{2}\cdot\dfrac{2}{99\cdot101}\\
=\dfrac{5}{2}\cdot\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{99\cdot101}\right)\\
=\dfrac{5}{2}\cdot\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\\
=\dfrac{5}{2}\cdot\left(1-\dfrac{1}{101}\right)\\
=\dfrac{5}{2}\cdot\dfrac{100}{101}\\
=\dfrac{250}{101}\)
B2
\(A=\dfrac{10^5+4}{10^5-1}=\dfrac{10^5-1+5}{10^5-1}=\dfrac{10^5-1}{10^5-1}+\dfrac{5}{10^5-1}=1+\dfrac{5}{10^5-1}\\
B=\dfrac{10^5+3}{10^5-2}=\dfrac{10^5-2+5}{10^5-2}=\dfrac{10^5-2}{10^5-2}+\dfrac{5}{10^5-2}=1+\dfrac{5}{10^5-2}
\)
Vì \(10^5-1>10^5-2\Rightarrow\dfrac{5}{10^5-1}< \dfrac{5}{10^5-2}\Rightarrow1+\dfrac{5}{10^5-1}< 1+\dfrac{5}{10^5-2}\Leftrightarrow A< B\)
MV
14 tháng 5 2017
B3
\(A=\dfrac{n-2}{n+3}\)
Để \(A\) có giá trị nguyên thì \(n-2⋮n+3\)
\(n-2=n+3+\left(-5\right)⋮n+3\Rightarrow-5⋮n+3\Rightarrow n+3\inƯ\left(-5\right)\)
\(Ư\left(-5\right)=\left\{-5;-1;1;5\right\}\)
| n+3 | -5 | -1 | 1 | 5 |
| n | -8 | -4 | -2 | 2 |
Vậy \(n\in\left\{-8;-4;-2;2\right\}\)
\(B=\dfrac{3n+1}{n-1}\)Để \(A\) có giá trị nguyên thì \(3n+1⋮n-1\)
\(3n+1=3n-3+4⋮n-1\Leftrightarrow3\cdot\left(n-1\right)+4⋮n-1\Rightarrow4⋮n-1\Rightarrow n-1\inƯ\left(4\right)\)
\(Ư\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)
| n-1 | -4 | -2 | -1 | 1 | 2 | 4 |
| n | -3 | -1 | 0 | 2 | 3 | 5 |
Vậy \(n\in\left\{-3;-1;0;2;3;5\right\}\)
T
25 tháng 3 2018
Bài nhìn vô muốn xỉu rồi ='((
1. a) \(\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{91.94}+\frac{2}{94.97}\)
\(=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{91.94}+\frac{3}{94.97}\right)\)
\(=\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{94}-\frac{1}{97}\right)\)
\(=\frac{2}{3}\left(1-\frac{1}{97}\right)=\frac{2}{3}.\frac{96}{97}=\frac{64}{97}\)
b) Bạn tự làm, làm nữa chắc xỉu =((( Khi nào rảnh mình sẽ làm, nếu bạn cần
2 )
a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{1005}{2011}\)
\(\Leftrightarrow\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{1005}{2011}\)
\(\Leftrightarrow\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{1005}{2011}\)
\(\Leftrightarrow1-\frac{1}{x+2}=\frac{1005}{2011}:2=\frac{1005}{4022}\)
\(\Leftrightarrow\frac{1}{x+2}=1-\frac{1005}{4022}=\frac{3017}{4020+2}\)
\(\Rightarrow x=4020\)
4 . 103 + 5 . 102 + 7 . 10
= 10 . (4 . 102 + 5 . 10 + 7)
= 10 . (400 + 50 + 7)
= 10 . 457
= 4570
4.103 + 5.102 + 7.10
= 4.10.102 + 5.102 + 70
= 40.102 + 5.102 + 70
= 102.(40 + 5) +70
= 100.45 + 70
= 4500 + 70
= 4570