Question

[Nguyễn Thanh Thủy]

Tìm x biết:

​​\(\frac{1}{10}+\frac{1}{40}+\frac{1}{88}+...+\frac{3}{\left(x+2\right)x\left(3x+5\right)}=\frac{3}{20}\)

giải giúp tôi nhé!arigator 

Answer 1

[l҉o҉n҉g҉ d҉z҉]

\(\text{Ta có: }\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+.....+\frac{3}{\left(x+2\right)\left(x+5\right)}=\frac{3}{20}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+.....+\frac{1}{\left(x+2\right)}-\frac{1}{\left(x+5\right)}=\frac{3}{20}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{\left(x+5\right)}=\frac{3}{20}\)

\(\Rightarrow\frac{1}{\left(x+5\right)}=\frac{1}{2}-\frac{3}{20}\)