Question

Tìm x \(\in\) N biết:

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

Giải được = 3 tick
 

Answer 1

\(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)

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

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

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

\(\frac{1}{\left(x+1\right)}=\frac{1}{6}-\frac{1}{9}=\frac{1}{18}\Leftrightarrow x+1=18\Leftrightarrow x=17\)

Answer 2

=>2/42+2/56+2/72+...+2/(x.(x+1))=2/9

=>2/(6*7)+2/(7*8)+2/(8*9)+......+2/((x+(x+1))=2/9

=>1/6-1/7+1/7-1/8+1/8-1/9+....+1/x-1/x+1=2/9

=>1/6-1/x+1=2/9

=>1/x+1=1/6-2/9

Tự làm tiếp nhé 

Answer 3

\(17\)