`A = 1/3 + 1/8 + 1/15 + 1/24 + 1/35 + 1/48 + 1/63 + 1/80`
`A = ( 1/3 + 1/15 + 1/35 + 1/63) + ( 1/8 + 1/24 + 1/48 +1/80)`
\(A=\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}\right)+\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+\dfrac{1}{8.10}\right)\)
\(A=\dfrac{1}{2}.\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}\right)+\dfrac{1}{2}.\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+\dfrac{2}{8.10}\right)\)
`A = 1/2 xx ( 1 - 1/3 + 1/3 - 1/5 + ....+ 1/7 - 1/9) + 1/2 xx ( 1/2 - 1/4 + 1/4 - 1/6 + ....+ 1/8 - 1/10)`
`A = 1/2 xx ( 1 - 1/9) + 1/2 xx ( 1/2 - 1/10)`
`A = 1/2 xx 8/9 + 1/2 xx 2/5`
`A = 1/2 xx ( 8/9 + 2/5)`
` A = 1/2 xx 58/45`
` A = 29/25`
` Vậy.....`
\(A=\dfrac{1}{3}+\dfrac{1}{8}+\dfrac{1}{15}+\dfrac{1}{24}+\dfrac{1}{35}+\dfrac{1}{48}+\dfrac{1}{63}+\dfrac{1}{80}\\ A=\dfrac{1}{1\times3}+\dfrac{1}{2\times4}+\dfrac{1}{3\times5}+\dfrac{1}{4\times6}+\dfrac{1}{5\times7}+\dfrac{1}{6\times8}+\dfrac{1}{7\times9}+\dfrac{1}{8\times10}\\ A\times2=\left(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}\right)+\left(\dfrac{2}{2\times4}+\dfrac{2}{4\times6}+\dfrac{2}{6\times8}+\dfrac{2}{8\times10}\right)\)\(A\times2=\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}\right)+\left(\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}\right)\\ A\times2=\dfrac{8}{9}+\dfrac{2}{5}\\ A\times2=\dfrac{58}{45}\\ A=\dfrac{29}{45}\)
