Đáp án:
Giải thích các bước giải:
`a) M = 1/1.2 + 1/2.3 + 1/3.4 +.......+ 1/99.100`
`-> M = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +.........+ 1/99 - 1/100`
`-> M = 1 - 1/100`
`-> M = 99/100`
`b, N = 2/3.5 + 2/5.7 + 2/7.9 +..........+ 2/37.39`
`-> N = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 +......+ 1/37 - 1/39`
`-> N = 1/3 - 1/39`
`-> N = 4/13`
`c, P = 1/10 + 1/15 + 1/21 +........+ 1/120`
`-> 2P = 2/20 + 2/30 + 2/42 +.......+ 2/240`
`-> 2P = 2/4.5 + 2/5.6 + 2/6.7 +......+ 2/15.16`
`-> 2P = 2 . ( 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 +........+ 1/15 - 1/16 )`
`-> P = 1/4 - 1/16`
`-> P = 3/16`
-Công thức tách: `k/(a.(a+k)) = 1/a - 1/(a+k) ( k in NN^** )`
`#Dung09`
