Đáp án+Giải thích các bước giải:
`a`. `1/1.3`+`1/3.5`+....+`1/19.21`
=`1/2`(`2/1.3`+`2/3.5`+....+`2/19.21`)
=`1/2`(`1/1`-`1/3`+`1/3`-`1/5`+...+`1/19`-`1/21`)
=`1/2`(`1/1`-`1/21`)
=`1/2`.`20/21`
=`10/21`
`b`. `A`=`1/1.3`+`1/3.5`+....+`1/(2n-1).(2n+1)``<` `1/2`
=`1/2`(`2/1.3`+`2/3.5`+....+`2/(2n-1).(2n+1)`)
=`1/2`(`1`-`1/2n+1`)<`1/2`
(`đpcm`)