Question

Tim X .

Cau 1 : x : ( \(\frac{1}{1\times3}\) + \(\frac{1}{3\times5}\) + ...... + \(\frac{1}{101\times103}\)) = 1

Cau 2 : (\(\frac{1}{1\times2}\) + \(\frac{1}{2\times3}\) + \(\frac{1}{3\times4}\) + ......... + \(\frac{1}{11\times12}\) ) \(\times\)  X = 2

cac ban giup minh nha. Minh dang can gap

 

 

 

 

Answer 1

Câu 1 :

\(x:\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{101.103}\right)=1\)

\(=>x:\left[\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{101}-\frac{1}{103}\right)\right]\) \(=1\)

\(=>x:\left[\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{103}\right)\right]=1\)

\(=>\) \(x:\frac{51}{103}=1\)

\(=>x=1.\frac{51}{103}=\frac{51}{103}\)

 

Answer 2

Câu 2 :

\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{12.13}\right).x=2\)

\(=>\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}\right).x=2\)

\(=>\left(\frac{1}{1}-\frac{1}{12}\right).x=2\)

\(=>\frac{11}{12}.x=2\)

\(=>x=2:\frac{11}{12}\)

\(=>x=\frac{24}{11}\)

Answer 3

cau b bang 24/11​

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Cau a bang 51/103

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