a) \(\dfrac{13}{20}+\dfrac{3}{5}+x=\dfrac{5}{6}\)

\(\Rightarrow\dfrac{5}{4}+x=\dfrac{5}{6}\)

\(\Rightarrow x=\dfrac{5}{6}-\dfrac{5}{4}\)

\(\Rightarrow x=\dfrac{-5}{12}\)

b) \(x+\dfrac{1}{3}=\dfrac{2}{5}-\dfrac{-1}{3}\)

\(\Rightarrow x+\dfrac{1}{3}=\dfrac{11}{15}\)

\(\Rightarrow x=\dfrac{11}{15}-\dfrac{1}{3}\)

\(\Rightarrow x=\dfrac{2}{5}\)

c)\(\dfrac{-5}{8}-x=\dfrac{-3}{20}-\dfrac{-1}{6}\)

\(\dfrac{-5}{8}-x=\dfrac{1}{60}\)

\(\Rightarrow x=\dfrac{-5}{8}-\dfrac{1}{60}\)

\(\Rightarrow x=\dfrac{-77}{120}\)

d) \(\dfrac{3}{5}-x=\dfrac{1}{4}+\dfrac{7}{10}\)

\(\Rightarrow\dfrac{3}{5}-x=\dfrac{19}{20}\)

\(\Rightarrow x=\dfrac{3}{5}-\dfrac{19}{20}\)

\(\Rightarrow x=\dfrac{-7}{20}\)

e) \(\dfrac{-3}{7}-x=\dfrac{4}{5}+\dfrac{-2}{3}\)

\(\Rightarrow\dfrac{-3}{7}-x=\dfrac{2}{15}\)

\(\Rightarrow x=\dfrac{-3}{7}-\dfrac{2}{15}\)

\(\Rightarrow x=\dfrac{-59}{105}\)

g) \(\dfrac{-5}{6}-x=\dfrac{7}{12}+\dfrac{-1}{3}\)

\(\Rightarrow\dfrac{-5}{6}-x=\dfrac{1}{4}\)

\(\Rightarrow x=\dfrac{-5}{6}-\dfrac{1}{4}\)

\(\Rightarrow x=\dfrac{-13}{12}\)

\(M=\frac{\left(\frac{3}{10}-\frac{4}{15}-\frac{7}{20}\right).\frac{5}{19}}{\left(\frac{1}{17}+\frac{1}{7}-\frac{-3}{35}\right).\frac{-4}{3}}\)

\(M=\frac{\left(\frac{1}{30}-\frac{7}{20}\right).\frac{5}{19}}{\left(\frac{24}{119}+\frac{3}{35}\right).\frac{-4}{3}}\)

\(M=\frac{\frac{-19}{60}.\frac{5}{19}}{\frac{171}{595}.\frac{-4}{3}}\)

\(M=\frac{-1}{12}:\frac{-228}{595}\)

\(M=\frac{595}{2736}\)

Ta có: 

\(M=\frac{\left(\frac{3}{10}-\frac{4}{15}-\frac{7}{20}\right)\times\frac{5}{19}}{\left(\frac{1}{17}+\frac{1}{7}-\frac{-3}{35}\right)\times\frac{-4}{3}}\)

\(M=\frac{\left(\frac{1}{30}-\frac{7}{20}\right)\times\frac{5}{19}}{\left(\frac{24}{119}+\frac{3}{35}\right)\times\frac{-4}{3}}\)

\(M=\frac{\frac{-19}{60}\times\frac{5}{19}}{\frac{171}{595}\times\frac{-4}{3}}\)

\(M=\frac{-1}{12}\div\frac{-228}{595}\)

\(M=\frac{595}{2736}\)

Vậy \(M=\frac{595}{2736}\)

uses crt;

var i,n:integer;

s:real;

begin

clrscr;

n:=1;

s:=0;

while (n<=10000) do 

begin

n:=n+2;

s:=s+1/n;

end;

writeln(s:4:2);

readln;

end.

i giúp em vớiiiiii

\(M=\dfrac{3}{1+2}+\dfrac{3}{1+2+3}+...+\dfrac{3}{1+2+...+2022}\)

\(=\dfrac{3}{\dfrac{2\left(2+1\right)}{2}}+\dfrac{3}{\dfrac{3\left(3+1\right)}{2}}+...+\dfrac{3}{\dfrac{2022\left(2022+1\right)}{2}}\)

\(=\dfrac{6}{2\left(2+1\right)}+\dfrac{6}{3\left(3+1\right)}+...+\dfrac{6}{2022\cdot2023}\)

\(=\dfrac{6}{2\cdot3}+\dfrac{6}{3\cdot4}+...+\dfrac{6}{2022\cdot2023}\)

\(=6\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{2022\cdot2023}\right)\)

\(=6\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2022}-\dfrac{1}{2023}\right)\)

\(=6\cdot\left(\dfrac{1}{2}-\dfrac{1}{2023}\right)=6\cdot\dfrac{2021}{4046}=\dfrac{12126}{4046}< 3\)

mà \(3< \dfrac{10}{3}\)

nên \(M< \dfrac{10}{3}\)

33333333333333333333

\(\frac{5}{3}-\frac{1}{4}+\frac{1}{3}-\frac{3}{4}\)

\(=\frac{5}{3}+\frac{-1}{4}+\frac{1}{3}+\frac{-3}{4}\)

\(=\left(\frac{5}{3}+\frac{1}{3}\right)+\left(\frac{-1}{4}+\frac{-3}{4}\right)\)

\(=\frac{6}{3}+\frac{-4}{4}\)

\(=2+\left(-1\right)\)

\(=1\)

\(5\frac{3}{4}:3+2\frac{1}{4}\times\frac{1}{3}-\frac{3}{8}\)

\(=\frac{23}{4}\times\frac{1}{3}+\frac{9}{4}\times\frac{1}{3}-\frac{3}{8}\)

\(=\left(\frac{23}{4}+\frac{9}{4}\right)\times\frac{1}{3}-\frac{3}{8}\)

\(=8\times\frac{1}{3}-\frac{3}{8}\)

\(=\frac{8}{3}-\frac{3}{8}\)

\(=\frac{55}{24}\)

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