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a) \(\frac{51}{3}-\frac{22}{3}=\frac{51-22}{3}=\frac{29}{3}\)
b) \(\frac{5}{12}+\frac{5}{6}-\frac{3}{4}=\frac{5}{12}+\frac{10}{12}-\frac{9}{12}=\frac{5+10-9}{12}=\frac{6}{12}=\frac{1}{2}\)
c) \(1-\left(\frac{1}{5}+\frac{1}{2}\right)=\frac{10}{10}-\frac{2}{10}-\frac{5}{10}=\frac{10-5-2}{10}=\frac{3}{10}\)
d) \(\frac{111}{4}-\left(\frac{25}{7}+\frac{51}{4}\right)=\frac{777}{28}-\frac{60}{28}-\frac{357}{28}=\frac{360}{28}=\frac{90}{7}\)
e) \(\left(\frac{85}{11}+\frac{35}{7}\right)-\frac{35}{11}=\left(\frac{85}{11}-\frac{35}{11}\right)+\frac{35}{7}=\frac{50}{11}-\frac{35}{7}=\frac{350}{77}-\frac{385}{77}=-\frac{35}{77}\)
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\(\frac{1}{5.8}+\frac{1}{8.11}+\frac{1}{11.14}+...+\frac{1}{26.29}\)
\(=\frac{1}{3}.\left(\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{26.29}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{26}-\frac{1}{29}\right)\)
\(=\frac{1}{3}.\left(\frac{1}{5}-\frac{1}{29}\right)\)
\(=\frac{1}{3}.\frac{24}{145}\)
\(=\frac{8}{145}\)
Đặt A=\(\frac{1}{5\times8}+\frac{1}{8\times11}+.......+\frac{1}{26\times29}\)
Ta có: 3A=\(\frac{3}{5\times8}+\frac{3}{8\times11}+....+\frac{3}{26\times29}\)
\(\Rightarrow3A=\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{26}-\frac{1}{29}\)
\(\Rightarrow3A=\frac{1}{5}-\frac{1}{29}\)
\(\Rightarrow A=\frac{24}{145}:3\)
\(\Rightarrow A=\frac{8}{145}\)
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- số số hạng của tổng là:
(15-1):2+1=8(số hạng)
Tổng trên có giá trị là:
(15+1).8:2=64
-số số hạng của tổng là:
(16-2):2+1=8(số hạng)
Tổng trên có giá trị là:
(16+2).8:2=72
-số số hạng của tổng là:
(22-1):3+1=8(số hạng)
Tổng trên có giá trị là:
(22+1).8:2=92
1+3+5+7+9+11+13+15=(1+15)+(3+13)+(5+11)+(7+9)=16x4=64
1+5+9+13+17+21+25+29+33+37=(1+37)+(5+33)+(9+29)+(13+25)+(17+21)=38x5=190
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\(1-x=\frac{29}{12}+\frac{32}{8}\)
\(\Rightarrow1-x=\frac{77}{12}\)
\(\Rightarrow x=1-\frac{77}{12}=\frac{-65}{12}\)
\(\frac{31}{8}.x-\frac{11}{4}=\frac{42}{12}.\frac{10}{8}-\frac{1}{3}\)
\(\Rightarrow\frac{31}{8}.x-\frac{11}{4}=\frac{35}{8}-\frac{1}{3}\)
\(\Rightarrow\frac{31}{8}.x-\frac{11}{4}=\frac{97}{24}\)
\(\Rightarrow\frac{31}{8}.x=\frac{97}{24}+\frac{11}{4}=\frac{163}{24}\)
\(\Rightarrow x=\frac{163}{24}:\frac{31}{8}=\frac{163}{93}\)
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Đặt A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{17.19}\)
\(\Rightarrow2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{17.19}\)
\(\Rightarrow2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{17}-\frac{1}{19}\)
\(\Rightarrow2A=1-\frac{1}{19}\)
\(\Rightarrow2A=\frac{18}{19}\)
\(\Rightarrow A=\frac{18}{19}.\frac{1}{2}=\frac{9}{19}\)
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{17.19}\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{19}\right)\)
\(=\frac{1}{2}.\frac{18}{19}=\frac{9}{19}\)