Question

2​/1.3+14/3.5+34/5.7+.......+322/17.19 =?​

Answer 1

= \(\frac{1.3-1}{1.3}+\frac{3.5-1}{3.5}+...+\frac{17.19-1}{17.19}=1-\frac{1}{1.3}+1-\frac{1}{3.5}+...+1-\frac{1}{17.19}\)

= \(\left(1+1+...+1\right)-\left(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{17.19}\right)\)

= \(9-\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{17.19}\right)=9-\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{17}-\frac{1}{19}\right)\)

= \(9-\frac{1}{2}.\left(1-\frac{1}{19}\right)=9-\frac{1}{2}.\frac{18}{19}=9-\frac{9}{19}=\frac{162}{19}\)