Question

(1/1.2.3+1/2.3.4+..............+1/8.9.10).x=23/45

nhờ các bn giải giúp tớ vs. Cảm ơn

Answer 1

\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{8.9.10}\right)x=\frac{23}{45}\)

\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)x=\frac{23}{45}\)

\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{9.10}\right)x=\frac{23}{45}\)

\(\Leftrightarrow\frac{1}{2}.\frac{22}{45}.x=\frac{23}{45}\)

\(\Leftrightarrow\frac{11}{45}x=\frac{23}{45}\)

\(\Rightarrow x=\frac{23}{11}\)

Answer 2

(1/1.2.3 +1/2.3.4 + ..... + 1/8.9.10).x=23/45

1/2 . (2/1.2.3 + ........+2 / 8.9.10).x=23/45

1/2.x(1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 +.....+1/8.9 - 1/9.10) = 23/45

1/2x(1/2-1/90) = 23/45

x . 22/45 = 23/45 :1/2

x = 46/45 :22/45

x = 23/11