Question

\(\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\right).x=1\)

Tính giùm tui

Answer 1

\(\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\right)x=1\)

\(\Rightarrow\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)x=1\)

\(\Rightarrow\left(\dfrac{1}{2}-\dfrac{1}{50}\right)x=1\)

\(\Rightarrow\dfrac{12}{25}x=1\)

\(\Rightarrow x=\dfrac{25}{12}\)

Vậy \(x=\dfrac{25}{12}\)

Answer 2

\(\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\right).x=1\)

Ta có: \(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\)

\(=\dfrac{3-2}{2.3}+\dfrac{4-3}{3.4}+...+\dfrac{50-49}{49.50}\)

\(=\dfrac{3}{2.3}-\dfrac{2}{2.3}+\dfrac{4}{3.4}-\dfrac{3}{3.4}+...+\dfrac{50}{49.50}-\dfrac{49}{49.50}\)

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

\(=\dfrac{1}{2}-\dfrac{1}{50}=\dfrac{12}{25}\)

\(\Rightarrow\dfrac{12}{25}.x=1\Rightarrow x=1:\dfrac{12}{25}=\dfrac{25}{12}=2\dfrac{1}{12}\)

Vậy \(x=\dfrac{25}{12}\) hay \(x=2\dfrac{1}{12}\)

Answer 3

\(\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\right)x=1\)

\(\Rightarrow\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)x=1\)

\(\Rightarrow\left(\dfrac{1}{2}-\dfrac{1}{50}\right)x=1\)

\(\Rightarrow\dfrac{12}{25}x=1\)

\(\Rightarrow x=\dfrac{25}{12}\)

Answer 4

\(\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=1:x\)

Hay \(1:x=\dfrac{1}{2}-\dfrac{1}{50}\)

\(1:x=\dfrac{23}{50}\)

\(x=\dfrac{23}{50}.1\)

\(x=\dfrac{23}{50}\)

Vậy \(x=\dfrac{23}{50}\)

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Answer 5

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Answer 6

\(\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\right)x=1\\ \Rightarrow\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+....+\dfrac{1}{49}-\dfrac{1}{50}\right)x=1\\ \Rightarrow\left(\dfrac{1}{2}-\dfrac{1}{50}\right)x=1\\ \Rightarrow\dfrac{12}{25}x=1\\ \Rightarrow x=\dfrac{25}{12}\)

Answer 7

\(\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right).x=1\)

\(\left(\dfrac{1}{2}-\dfrac{1}{50}\right).x=1\)

\(\dfrac{12}{25}.x=1\)

x = 1: \(\dfrac{12}{25}\)

x = \(\dfrac{25}{12}\)

Vậy x = \(\dfrac{25}{12}\)

Answer 8

(\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\)).x=1

=(\(\dfrac{1}{2}+\dfrac{1}{50}\)).x=1

=\(\dfrac{25}{12}\).X=1

\(\Rightarrow\)x=1:\(\dfrac{25}{12}\)

\(\Rightarrow\)x=\(\dfrac{12}{25}\)

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