Question

  x + ( x + 1/2 ) + ( x + 1/6 ) + ( x + 1/12 )+...+( x + 1/9900) = 2 

 

 

Answer 1

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

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

 => \(\left(x+x+x+...+x\right)+\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)=2\)(100 hạng tử x)

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

=>  \(100x+1-\frac{1}{100}=2\)

=> \(100x+\frac{99}{100}=2\)

=> \(100x=\frac{101}{100}\)

=> \(x=\frac{101}{10000}\)