Tính a.1/2+1/2.3+1/4.5+….+1/99.100 b.1/2.4+1/4.6+…+1/98.100 Mn lm chi tiết jup mk vs Mk đg cần gấp 28/08/2021 Bởi Madeline Tính a.1/2+1/2.3+1/4.5+….+1/99.100 b.1/2.4+1/4.6+…+1/98.100 Mn lm chi tiết jup mk vs Mk đg cần gấp
`\text{Chủ tus sửa lại đề : }` `a ) 1/2 + 1/2.3 + 1/3.4 + 1/4.5 + … + 1/99.100` `= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + … + 1/99.100` `= 1 – ( 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/99 – 100)` `= 1 – 1/100` `= 100/100 – 1/100` `= 99/100` `b ) 1/2.4+1/4.6+…+1/98.100` `= 1/2 . ( 2/2.4 + 2/4.6 + … + 2/98.100 )` `= 1/2 . ( 1/2 – 1/4 + 1/4 – 1/6 + … + 1/98 – 1/100 )` `= 1/2 . ( 1/2 – 1/100 )` `= 1/2 . ( 50/100 – 1/100 )` `= 1/2 . 49/100` `=49/200` Bình luận
`\text{Chủ tus sửa lại đề : }`
`a ) 1/2 + 1/2.3 + 1/3.4 + 1/4.5 + … + 1/99.100`
`= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + … + 1/99.100`
`= 1 – ( 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/99 – 100)`
`= 1 – 1/100`
`= 100/100 – 1/100`
`= 99/100`
`b ) 1/2.4+1/4.6+…+1/98.100`
`= 1/2 . ( 2/2.4 + 2/4.6 + … + 2/98.100 )`
`= 1/2 . ( 1/2 – 1/4 + 1/4 – 1/6 + … + 1/98 – 1/100 )`
`= 1/2 . ( 1/2 – 1/100 )`
`= 1/2 . ( 50/100 – 1/100 )`
`= 1/2 . 49/100`
`=49/200`
Đáp án:
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