Question

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A =\(\frac{1}{1}\)+ \(\frac{1}{3}\)+ \(\frac{1}{6}\)+ \(\frac{1}{10}\)+.....+\(\frac{1}{4851}\)+ \(\frac{1}{4950}\)

 

Answer 1

#)Giải :

\(A=1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{4950}\)

\(2A=2+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)

\(2A=2+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(2A=2+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(2A=2+\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(\Leftrightarrow A=1+\left(1-\frac{1}{50}\right)\)

\(\Leftrightarrow A=\frac{99}{50}\)

Answer 2

\(A=1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{4851}+\frac{1}{4950}\)

   \(=2.\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9702}+\frac{1}{9900}\right)\)

   \(=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{98.99}+\frac{1}{99.100}\right)\) 

    \(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{1000}\right)\)

    \(=2.\left(1-\frac{1}{100}\right)\)

     \(=2.\frac{99}{100}\)

     \(=\frac{99}{50}\)

Answer 3

\(\Rightarrow\frac{1}{2}A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9702}+\frac{1}{9900}\)

\(\Leftrightarrow\frac{1}{2}A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(\Leftrightarrow\frac{1}{2}A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Leftrightarrow\frac{1}{2}A=1-\frac{1}{100}=\frac{99}{100}\Rightarrow A=\frac{99}{50}\)