Đề sai nhé bạn!

Đề sai chỗ \(\dfrac{11}{12.23}\) nha mấy bạn mk nghi nhầm

đề sai sao làm bạn nên sửa cho bọn tui nha

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\(\Rightarrow\frac{11}{12}+\frac{11}{12}-\frac{11}{23}+...+\frac{11}{89}-\frac{11}{100}+x=\frac{2}{3}\)

\(\Rightarrow\frac{1}{12}+\frac{1}{12}-\frac{1}{23}+...+\frac{1}{89}-\frac{1}{100}+x=\frac{2}{3}\)

\(\Rightarrow\frac{1}{12}-\frac{1}{100}+x=\frac{2}{3}\)

\(\Rightarrow\frac{11}{150}+x=\frac{2}{3}\)

=>\(x=\frac{2}{3}-\frac{11}{150}\)

=>x=\(\frac{89}{150}\)

Ta có:

\(\left(\dfrac{11}{12}+\dfrac{11}{12.23}+\dfrac{11}{23.34}+...+\dfrac{11}{89.100}\right)+x=\dfrac{2}{3}\)

\(\Leftrightarrow\left(\dfrac{11}{1.12}+\dfrac{11}{12.23}+\dfrac{11}{23.34}+...+\dfrac{11}{89.100}\right)+x=\dfrac{2}{3}\)

\(\Leftrightarrow\left(1-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{23}+...+\dfrac{1}{89}-\dfrac{1}{100}\right)+x=\dfrac{2}{3}\)

\(\Leftrightarrow\left(1-\dfrac{1}{100}\right)+x=\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{99}{100}+x=\dfrac{2}{3}\)

\(\Leftrightarrow x=\dfrac{2}{3}-\dfrac{99}{100}=\dfrac{-97}{300}\)

Vậy \(x=\dfrac{-97}{300}\)

\(\left(\frac{11}{1.12}+\frac{11}{12.23}+...+\frac{11}{89.100}\right)+x=\frac{5}{3}\)

\(\Leftrightarrow\left(\frac{1}{1}-\frac{1}{12}+\frac{1}{12}-\frac{1}{23}+...+\frac{1}{89}-\frac{1}{100}\right)+x=\frac{5}{3}\)

\(\Leftrightarrow\left(1-\frac{1}{100}\right)+x=\frac{5}{3}\Leftrightarrow\frac{99}{100}+x=\frac{5}{3}\Leftrightarrow x=\frac{5}{3}-\frac{99}{100}\)

\(\Leftrightarrow x=\frac{297}{300}=\frac{ }{100}\)

mk nhầm \(x=\frac{203}{300}\)