\(A=\dfrac{1}{1.3}+\dfrac{1}{2.4}+\dfrac{1}{3.5}+...+\dfrac{1}{7.9}+\dfrac{1}{8.10}\)
\(A=\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{7.9}\right)+\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{8.10}\right)\)
\(2A=\dfrac{1}{2}\left[1-\dfrac{1}{9}+\left(\dfrac{1}{2}-\dfrac{1}{10}\right)\right]\)
\(2A=\dfrac{1}{2}\left(\dfrac{8}{9}+\dfrac{2}{5}\right)\)
\(2A=\dfrac{1}{2}.\dfrac{58}{45}\)
\(2A=\dfrac{29}{45}\)
\(A=\dfrac{29}{45}:2=\dfrac{29}{90}\)
A= 1/1.3+1/2.4+1/3.5+...+1/7.9+1/8.10
A = (1/1.3+1/3.5 + 1/5.7 + 1/7.9) + (1/2.4 + 1/4.6 + 1/6.8 + 1/8.10)
A = 1/2. (2/1.3+2/3.5 + 2/5.7 + 2/7.9) + 1/2. (2/2.4 + 2/4.6 + 2/6.8 + 2/8.10)
A= 1/2.(1-1/9) + 1/2.(1/2-1/10)
A = 1/2.8/9 + 1/2.2/5
A = 4/9 + 1/5
A = 20/45 + 9 /45
A = 29/45