Đáp án: `A = 361/770`
Giải thích các bước giải:
`A = 1/3 + 1/150 + 1/15 + 1/300 + 1/35 + 1/500 + 1/63 + 1/750 + 1/99 + 1/1050`
`= (1/3 + 1/15 + 1/35 + 1/63 + 1/99) + (1/150 + 1/300 + 1/500 + 1/750 + 1/1050)`
`= ( 1/(1.3) + 1/(3.5) + 1/(5.7) + 1/(7.9) + 1/(9.11) ) + ( 1/(10.15) + 1/(15.20) + 1/(20.25) + 1/(25.30) + 1/(30.35)`
`= 1/2 . (1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11) + 1/5 . (1/10 - 1/15 + 1/15 - 1/20 + 1/20 - 1/25 + 1/25 - 1/30 + 1/30 - 1/35)`
`= 1/2 . (1 - 1/11) + 1/5 . (1/10 - 1/35)`
`= 1/2 . 10/11 + 1/5 . 1/14`
`= 5/11 + 1/70`
`= 350/770 + 11/770`
`= 361/770`