Đáp án:
Câu `7:`
`a,` `1/(1xx2)+1/(2xx3)+1/(3xx4)+1/(4xx5)+...+1/(98xx99)+1/(99xx100)`
`=(2-1)/(1xx2)+(3-2)/(2xx3)+(4-3)/(3xx4)+(5-4)/(4xx5)+...+(99-98)/(98xx99)+(100-99)/(99xx100)`
`=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100`
`=1-1/100`
`=99/100`
`b,` `1/6+1/12+1/20+1/30+1/42+...+1/90+1/110`
`=1/(2xx3)+1/(3xx4)+1/(4xx5)+1/(5xx6)+1/(6xx7)+...+1/(9xx10)+1/(10xx11)`
`=(3-2)/(2xx3)+(4-3)/(3xx4)+(5-4)/(4xx5)+(6-5)/(5xx6)+(7-6)/(6xx7)+...+(10-9)/(9xx10)+(11-10)/(10xx11)`
`=1/2-1/3+1/3-1/4+1/4-1/5+1/5-/6+1/6-1/7+...+1/9-1/10+1/10-1/11`
`=1/2-1/11`
`=9/22`
`c,` `2/(11xx13)+2/(13xx15)+2/(15xx17)+...+2/(97xx99)`
`=(13-11)/(11xx13)+(15-13)/(13xx15)+(17-15)/(15xx17)+...+(99-97)/(97xx99)`
`=1/11-1/13+1/13-1/15+1/15-1/17+...+1/97-1/99`
`=1/11-1/99`
`=8/99`
`d,` `3/(5xx7)+3/(7xx9)+...+3/(41xx43)+3/(43xx45)`
`=3/2xx(2/(5xx7)+2/(7xx9)+...+2/(41xx43)+2/(43xx45))`
`=3/2xx((7-5)/(5xx7)+(9-7)/(7xx9)+...+(43-41)/(41xx43)+(45-43)/(43xx45))`
`=3/2xx(1/5-1/7+1/7-1/9+...+1/41-1/43+1/43-1/45)`
`=3/2xx(1/5-1/45)`
`=3/2xx8/45`
`=4/15`
