Question

2/6+2/12+2/20+...+2/x(x+1)=4/5

tìm x

Answer 1

TA có: \(\frac26+\frac{2}{12}+\cdots+\frac{2}{x\left(x+1\right)}=\frac45\)

=>\(\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\cdots+\frac{2}{x\left(x+1\right)}=\frac45\)

=>\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\ldots+\frac{1}{x\left(x+1\right)}=\frac25\)

=>\(\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{x}-\frac{1}{x+1}=\frac25\)

=>\(\frac12-\frac{1}{x+1}=\frac25\)

=>\(\frac{1}{x+1}=\frac12-\frac25=\frac{5-4}{10}=\frac{1}{10}\)

=>x+1=10

=>x=9