Mọi người giúp em với ạ!

`1`

`a, 1/[1 xx 2] + 1/[2 xx 3] + ... + 1/[99 xx 100] `

`= 1 - 1/2 + 1/2 - 1/3 + ... + 1/99 - 1/100`

`= 1 - 1/100`

`= 99/100`

`b, 3/[5 xx 8] + 3/[8 xx 11] + 3/[11 xx 14] + ... + 3/[ 602 xx 605]`

`= 1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 + ... + 1/602 - 1/605`

`= 1/5 - 1/605`

`=24/121`

`c, 4/[3 xx 7] + 5/[7 xx 12] + 1/[12 xx 13] + 7/[ 13 xx 20] + 3/[20 xx 23]`

`= 1/3 - 1/7 + 1/7 - 1/12 + 1/12 - 1/13 + 1/13 - 1/20 + 1/20 - 1/23`

`= 1/3 - 1/23 = 20/69`

Đáp án+Giải thích các bước giải:

`a)1/[1xx2]+1/[2xx3]+...+1/[99xx100]`

`=(1-1/2)+(1/2-1/3)+...+(1/99-1/100)`

`=1-1/2+1/2-1/3+...+1/99-1/100`

`=1-1/100`

`=100/100-1/100`

`=99/100`

`---`

`b)3/[5xx8]+3/[8xx11]+3/[11xx14]+...+3/[602xx605]`

`=(1/5-1/8)+(1/8-1/11)+(1/11-1/14)+...+(1/602-1/605)`

`=1/5-1/8+1/8-1/11+1/11-1/14+...+1/602-1/605`

`=1/5-1/605`

`=121/605-1/605`

`=120/605`

`=24/121`

`---`

`c)4/[3xx7]+5/[7xx12]+1/[12xx13]+7/[13xx20]+3/[20xx23]`

`=(1/3-1/7)+(1/7-1/12)+(1/12-1/13)+(1/13-1/20)+(1/20-1/23)`

`=1/3-1/7+1/7-1/12+1/12-1/13+1/13-1/20+1/20-1/23`

`=1/3-1/23`

`=23/69-3/69`

`=20/69`

`----------`

Áp dụng:

`n/[n(n+1)]=1/n-1/[n+1]`