1.Tính

\(E=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(E=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(E=\frac{1}{1}-\frac{1}{50}\)

\(E=\frac{49}{50}\)

Câu 2 mình không biết, xin lỗi nha

E=1/1-1/2+1/2-1/3+1/3-1/4+...+1/49-1/50

  =1/1-1/50=49/50

1.
\(E=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)
\(E=\frac{1}{1}-\frac{1}{50}=\frac{49}{50}\)
2.
\(x+\frac{1}{6}=\frac{x}{3}\)
\(\frac{1}{6}=\frac{x}{3}-x=x\left(\frac{1}{3}-1\right)\)
\(\frac{1}{6}=-\frac{2}{3}x\Rightarrow x=\frac{1}{6}:-\frac{2}{3}=-\frac{1}{4}\)

(1-1/2).(1-1/3).(1-1/4)...(1-1/2002).x=1-1/1.2-1/2.3-1/3.4-...-1/2002.2003 ghi loi giai nha ae

\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2021}{2022}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{2021}{2022}\)

\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{2022}\)

=>x+1=2022

hay x=2021

\(\Rightarrow\left(x+x+...+x\right)+\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2022.2023}\right)=2023x\)

\(\Rightarrow2022x+\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-...-\dfrac{1}{2021}+\dfrac{1}{2021}-\dfrac{1}{2022}+\dfrac{1}{2022}-\dfrac{1}{2023}\right)=2023x\)\(\Rightarrow2022x-2023x=-\left(1-\dfrac{1}{2023}\right)\)

\(\Rightarrow-x=-\dfrac{2022}{2023}\Leftrightarrow x=\dfrac{2022}{2023}\)

(x + 1/1.2) + (x + 1/2.3) + (x + 1/3.4) + ... + (x + 1/2022.2023) = 2023x

x + x + x + ... + x + 1/1.2 + 1/2.3 + ... + 1/2022.2023 = 2023x

2022x + 1 - 1/2 + 1/2 - 1/3 + ... + 1/2022 - 2023 = 2023x

2023x - 2022x = 1 - 1/2023

x = 2022/2023

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

\(\frac{2}{3}x-\frac{1}{3}=\frac{1}{2}-\frac{2}{3}\)

\(\frac{2}{3}x-\frac{1}{3}=\frac{-1}{6}\)

\(\frac{2}{3}x=\frac{-1}{6}+\frac{1}{3}\)

\(\frac{2}{3}x=\frac{1}{6}\)

\(x=\frac{1}{6}:\frac{2}{3}\)

\(x=\frac{1}{4}\)

~ Hok tốt ~

\(\frac{3}{x+5}=15\%\)

\(\Leftrightarrow\frac{3}{x+5}=\frac{15}{100}\)

\(\Leftrightarrow\frac{3}{x+5}=\frac{3}{20}\)

\(\Leftrightarrow x+5=20\)

\(\Leftrightarrow x=20-5\)

\(\Leftrightarrow x=15\)

Giúp mình nha

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x.\left(x+1\right)}=201\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=201\)

\(1-\frac{1}{x+1}=201\)

\(\frac{1}{x+1}=1-201\)

\(\frac{1}{x+1}=-200\)

\(\Rightarrow x+1=-\frac{1}{200}\)

\(x=-\frac{1}{200}-1\)

\(x=-\frac{201}{200}\)

Vậy \(x=-\frac{201}{200}\)