a,\(2\frac{2}{9}x=\frac{1}{12}+\frac{1}{20}+............+\frac{1}{72}\)
=>\(\frac{20}{9}x=\frac{1}{3.4}+\frac{1}{4.5}+.............+\frac{1}{8.9}\)
=>\(\frac{20}{9}x=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.............+\frac{1}{8}-\frac{1}{9}\)
=>\(\frac{20}{9}x=\frac{1}{3}-\frac{1}{9}\)
=>\(\frac{20}{9}x=\frac{2}{9}\)
=>x=\(\frac{1}{10}\)
b,\(\left(\frac{1}{2.3}+\frac{1}{3.4}+.............+\frac{1}{45.50}\right)x=1\)
=>\(\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...........+\frac{1}{45}-\frac{1}{50}\right)x=1\)
=>\(\left(\frac{1}{2}-\frac{1}{50}\right)x=1\)
=>\(\frac{12}{25}x=1\)
=>\(x=\frac{25}{12}\)