Question

Tìm x \(\in\)N 

\(\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{x.\left(x+1\right)}=\frac{13}{90}\)

giúp mik nha các bn giải chi tiết ra nhé các bài kia cx vậy nha 

Answer 1

\(\text{Ta có: }\frac{1}{5.6}+\frac{1}{6.7}+.....+\frac{1}{x.\left(x+1\right)}=\frac{13}{90}\)

\(\Leftrightarrow\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+.....+\frac{1}{x}-\frac{1}{\left(x+1\right)}=\frac{13}{90}\)

\(\Leftrightarrow\frac{1}{5}-\frac{1}{x+1}=\frac{13}{90}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{5}-\frac{13}{90}\)

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

=> x + 1 = 18

=> x = 17