Bài làm :
Cách 1 :
`D=1/(2.4)+1/(4.6)+1/(6.8)+...+1/(100.102)`
`2D=2.(1/(2.4)+1/(4.6)+1/(6.8)+...+1/(100.102))`
`2D=2/(2.4)+2/(4.6)+2/(6.8)+...+2/(100.102)`
`2D=1/2-1/4+1/4-1/6+1/6-1/8+....+1/100-1/102`
`2D=1/2+(-1/4+1/4)+(-1/6+1/6)+(-1/8+1/8)+....+(-1/100+1/100)-1/102`
`2D=1/2-1/102`
`2D=51/102-1/102`
`2D=25/51`
`->D=25/51:2=25/102`
Vậy `D=25/102`
Cách 2 :
`D=1/(2.4)+1/(4.6)+1/(6.8)+...+1/(100.102)`
`D=1/2 . (2/(2.4)+2/(4.6)+2/(6.8)+...+2/(100.102))`
`D=1/2 . (1/2-1/4+1/4-1/6+1/6-1/8+...+1/100-1/102)`
`D=1/2 . [1/2 +(-1/4+1/4)+(-1/6+1/6)+(-1/8+1/8)+...+(-1/100+1/100)-1/102]`
`D=1/2 . (1/2-1/102)`
`D=1/2 . (51/102-1/102)`
`D=1/2 . 25/51`
`D=25/102`
Vậy `D=25/102`
