Question

Tìm x biết:

1/21+1/28+1/36+...+2/x.(x+1)=2/9

Ai giải hộ em với

Answer 1

<=> \(\frac{1}{3.7}+\frac{1}{4.7}+\frac{1}{4.9}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

<=> \(\frac{2}{2.3.7}+\frac{2}{2.4.7}+\frac{2}{2.4.9}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

<=> \(\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

<=> \(2.\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{\frac{x-1}{x+1}}=\frac{2}{9}\right)\)

<=> \(2.\left(\frac{1}{6}-\frac{\frac{1}{x-1}}{x+1}\right)=\frac{2}{9}\)

<=> \(\frac{1}{6}+\frac{1}{x+1}=\frac{1}{9}\)

<=> \(\frac{1}{x-1}=\frac{1}{6}-\frac{1}{9}\)

<=> \(\frac{1}{x+1}=\frac{1}{18}\)

<=> x + 1 = 18 

=> x = 18 - 1 

x  = 17