Question

[NGUYỄN ĐÌNH AN 6A5]

Tìm x biết :

\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{1}{X\left(X+2\right)}=\frac{2}{9}\)

\(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

Answer 1

[Thắng Nguyễn]

a)\(\frac{2}{42}+\frac{2}{56}+...+\frac{2}{x\left(x+2\right)}=\frac{2}{9}\)

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

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

\(\frac{1}{6}-\frac{1}{x+2}=\frac{2}{9}:2\)

\(\frac{1}{x+2}=\frac{1}{6}-\frac{1}{9}\)

\(\frac{1}{x+2}=\frac{1}{18}\)

=>x+2=18

=>x=16

b tương tự nhân nó với 1/2

Answer 2

[NGUYỄN ĐÌNH AN 6A5]

Cám ơn bạn