1/10x(2/9x9/2)x(3/8x8/3)x(5/6x6/5)=1/10x1x1x1=1/10

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+..+\frac{1}{x\left(x+2\right)}=\frac{20}{41}\)

\(\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{x.\left(x+2\right)}\right)=\frac{20}{41}\)

\(\frac{1}{2}\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{\left(x+2\right)-x}{x\left(x+2\right)}\right)=\frac{20}{41}\)

\(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{20}{41}\)

\(\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{20}{41}\)

\(1-\frac{1}{x+2}=\frac{20}{41}:\frac{1}{2}\)

\(1-\frac{1}{x+2}=\frac{40}{41}\)

\(\frac{1}{x+2}=1-\frac{40}{41}\)

\(\frac{1}{x+2}=\frac{1}{41}\)

\(x+2=41\)

\(x=41-2\)

\(x=39\)

Tìm x 

a) \(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{x\times\left(x+2\right)}=\frac{20}{41}\)

\(\Rightarrow\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+1\right)}\right)=\frac{20}{41}\)

\(\Rightarrow\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{20}{41}:\frac{1}{2}\)

\(\Rightarrow\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{40}{41}\)

\(\Rightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{\left(x+2\right)}=\frac{40}{41}\)

\(\Rightarrow1-\frac{1}{x+2}=\frac{40}{41}\)

\(\Rightarrow\frac{1}{x+2}=1-\frac{40}{41}\)

\(\Rightarrow\frac{1}{x+2}=\frac{1}{41}\)

\(\Rightarrow x+2=41\)

\(\Rightarrow x=41-2\)

\(\Rightarrow x=39\)

Vậy x = 39

\(2x\frac{1}{2}x3x\frac{1}{3}x4x\frac{1}{4}x5x\frac{1}{5}\)

\(=\left(2x\frac{1}{2}\right)x\left(3x\frac{1}{3}\right)x\left(4x\frac{1}{4}\right)x\left(5x\frac{1}{5}\right)\)

\(=\frac{2}{2}x\frac{3}{3}x\frac{4}{4}x\frac{5}{5}\)

\(=1x1x1x1\)

\(=1\)

Chúc bạn học tốt !!! 

11 nhân 23

\(\left[12\cdot15-x\right]\cdot\frac{1}{4}=120\cdot\frac{1}{4}\)

\(\Leftrightarrow\left[180-x\right]\cdot\frac{1}{4}=30\)

\(\Leftrightarrow180-x=30:\frac{1}{4}\)

\(\Leftrightarrow180-x=120\)

\(\Leftrightarrow x=60\)

tl moi cau

\(\left[x\cdot0,25+2012\right]\cdot2013=\left[50+2012\right]\cdot2013\)

\(\Leftrightarrow x\cdot0,25\cdot2013+2012\cdot2013=2062\cdot2013\)

\(\Leftrightarrow x\cdot\frac{2013}{4}+4050156=4150806\)

\(\Leftrightarrow x\cdot\frac{2013}{4}=100650\)

\(\Leftrightarrow x=100650:\frac{2013}{4}=100650\cdot\frac{4}{2013}=200\)

\(=\frac{1}{5}\times\frac{1}{3}\times\frac{3}{7}\times\frac{1}{2}\)

\(=\left(\frac{1}{5}\times\frac{1}{2}\right)\times\left(\frac{1}{3}\times\frac{3}{7}\right)\)

\(=\frac{1}{10}\times\frac{1}{7}\)

\(=\frac{1}{70}\)

Bạn dùng công thức này mà làm nhé :\(\frac{n}{a\times\left(a+n\right)}=\frac{1}{a}-\frac{1}{a+n}\)

Ví dụ :\(\frac{2}{3\times5}=\frac{1}{3}-\frac{1}{5};\frac{3}{4\times7}=\frac{1}{4}-\frac{1}{7};\frac{5}{6\times11}=\frac{1}{6}-\frac{1}{11}\)

Gửi kết bn với mh nhé!

ban ko tra loi ho minh cau nay a 

neu the minh ket ban kieu gi

194/175

co ai giai giup  minh voi please!

ban oi cu the