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\(\left(x-20\right)\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{200}}{\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+...+\frac{198}{2}+\frac{199}{1}}=\frac{1}{2000}\)
\(\left(x-20\right)\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{200}}{\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+....+\left(\frac{198}{2}+1\right)+1}=\frac{1}{2000}\)
\(\left(x-20\right)\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{200}}{\frac{200}{200}+\frac{200}{199}+\frac{200}{198}+....+\frac{200}{2}}=\frac{1}{2000}\)
\(\left(x-20\right)\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{200}}{200\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{200}\right)}=\frac{1}{2000}\)
\(\left(x-20\right).\frac{1}{200}=\frac{1}{2000}\)
\(\left(x-20\right)=\frac{1}{2000}:\frac{1}{200}=\frac{1}{2000}.200=\frac{1}{10}\)
\(\Rightarrow x=\frac{1}{10}+20=\frac{201}{10}\)
Đề: X=\(\frac{1}{1+2}\)+\(\frac{1}{1+2+3}\)+.......+\(\frac{1}{1+2+3+4+20}\)
X=\(\frac{1}{2.3:2}\)+\(\frac{1}{3.4:2}\)+\(\frac{1}{4.5:2}\)+......+\(\frac{1}{20.21:2}\)
X=\(\frac{2}{2.3}\)+\(\frac{2}{3.4}\)\(\frac{2}{4.5}\)+........+\(\frac{2}{20.21}\)
X=2.(\(\frac{1}{2}\).3+\(\frac{1}{3}\).4+\(\frac{1}{4}\).5+.....+\(\frac{1}{20}\).21)
X=2.(\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+......+\(\frac{1}{20}\)-\(\frac{1}{21}\))
X=2.(\(\frac{1}{2}\)-\(\frac{1}{21}\))
X=2.(\(\frac{21}{42}\)-\(\frac{2}{42}\))
X=2.\(\frac{19}{42}\)
X=\(\frac{19}{21}\)
Mn xem thử đúng ko nha!
Ta có: \(1+2=\frac{2.3}{2}\); \(1+2+3=\frac{3.4}{2}\); .......... ; \(1+2+3+....+20=\frac{20.21}{2}\)
\(\Rightarrow X=\frac{1}{\frac{2.3}{2}}+\frac{1}{\frac{3.4}{2}}+.......+\frac{1}{\frac{20.21}{2}}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+........+\frac{2}{20.21}=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{20.21}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..........+\frac{1}{20}-\frac{1}{21}\right)=2.\left(\frac{1}{2}-\frac{1}{21}\right)=2.\frac{19}{42}=\frac{19}{21}\)
Ta có: \(x-\frac{20}{11\cdot13}-\frac{20}{13\cdot15}-...-\frac{20}{53\cdot55}=\frac{3}{11}\)
\(\Leftrightarrow x-10\cdot\left(\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+...+\frac{2}{53\cdot55}\right)=\frac{3}{11}\)
\(\Leftrightarrow x-10\cdot\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow x-10\cdot\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)
\(\Leftrightarrow x-10\cdot\frac{4}{55}=\frac{3}{11}\)
\(\Leftrightarrow x-\frac{8}{11}=\frac{3}{11}\)
\(\Leftrightarrow x=\frac{3}{11}+\frac{8}{11}\)
\(\Leftrightarrow x=1\)
Vậy \(x=1\)thỏa mãn đề.
Ta có
1+1/2(1+2)+....+1/20(1+2+3+...+20)
= 2/2+3/2+.....+19/2
=(2+3+....+19)/2
= 189/2
a, Đề có vẻ sai sai nhé :v
b, \(\left|\frac{1}{2}x-\frac{2}{3}\right|-1=\frac{1}{6}\)
\(\Leftrightarrow\left|\frac{1}{2}x-\frac{2}{3}\right|=\frac{7}{6}\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}x-\frac{2}{3}=\frac{7}{6}\\\frac{1}{2}x-\frac{2}{3}=-\frac{7}{6}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{11}{3}\\x=-1\end{cases}}\)
Vậy : ....
c, \(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x(x+1)}=\frac{4}{5}\)
\(\Leftrightarrow\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+...+\frac{2}{x\cdot(x+1)}=\frac{4}{5}\)
\(\Leftrightarrow2\left[\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right]=\frac{4}{5}\)
\(\Leftrightarrow2\left[\frac{1}{2}-\frac{1}{x+1}\right]=\frac{4}{5}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2}{5}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{10}\)
\(\Leftrightarrow x+1=10\Leftrightarrow x=9\)
Vậy x = 9
\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{19}{20}=\frac{1}{20}\)
\(B=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{20}\right)\)
\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{19}{20}\)
\(B=\frac{1}{20}\)
Đặt biểu thức là A, ta có:
\(A=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+...+\frac{1}{20}.\left(1+2+3+...+20\right)\)
\(A=1+\frac{1}{2}.2.3:2+\frac{1}{3}.3.4:2+...+\frac{1}{20}.20.21:2=\frac{2}{2}+\frac{3}{2}+...+\frac{21}{2}\)
\(A=\frac{2+3+4+...+21}{2}=\frac{230}{2}=115\)
=2/2+3/2+4/2+.....+19/2
=(2+3+4+.....+19)/2
=189/2