Question

Tìm số tự nhiên x biết: \(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right)x=\frac{22}{45}\)

Answer 1

\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right)x=\frac{22}{45}\)

\(\Rightarrow\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right)x=\frac{22}{45}\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)x=\frac{22}{45}\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{2}-\frac{1}{90}\right)x=\frac{22}{45}\)

\(\Rightarrow\frac{22}{45}x=\frac{44}{45}\)

\(\Rightarrow x=\frac{44}{45}:\frac{22}{45}\)

\(\Rightarrow x=2\)

Vậy x = 2

Answer 2

\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{8.9.10}\right)x=\frac{22}{45}\)

\(\Rightarrow\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right):2=\frac{22}{45}:x\)

\(\Rightarrow\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right):2=\frac{22}{45}:x\)

\(\Rightarrow\left(\frac{1}{1.2}-\frac{1}{9.10}\right):2=\frac{22}{45}:x\)

\(\Rightarrow\left(\frac{1}{2}-\frac{1}{90}\right):2=\frac{22}{45}:x\)

\(\Rightarrow\frac{22}{45}:2=\frac{22}{45}:x\)

\(\Rightarrow x=2\)