Tính `1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132+1/156+1/182+1/210+1/240+1/272` 13/07/2021 Bởi Harper Tính `1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132+1/156+1/182+1/210+1/240+1/272`
Đáp án: Giải thích các bước giải: `1 + 1/2 + 1/6 + 1/12 + … + 1/240 + 1/272` `= 1 + 1/(1 . 2) + 1/(2 . 3) + ..+ 1/(15 . 16) + 1/(16 . 17)` `= 1 + (2 – 1)/(1 . 2) + (3 – 2)/(2 . 3) + ..+ (16 – 15)/(15 . 16) + (17 – 16)/(16 . 17)` `= 1 + 1 – 1/2 + 1/2 – 1/3 + 1/3 – ….+ 1/15 – 1/16 + 1/16 – 1/17` `= 1 + 1 – 1/17` `= 2 – 1/17` `= 34/17 – 1/17` `= 33/17` Bình luận
`1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132+1/156+1/182+1/210+1/240+1/272` =`1+1/1.2+1/2.3+1/3.4+1/4.5+……+1/15.16+1/16.17` =`1+(1-1/2+1/2-1/3+1/3-1/4+…..+1/15-1/16+1/16-1/17)` =`1+1-1/17` =`2-1/17` =`33/17` Bình luận
Đáp án:
Giải thích các bước giải:
`1 + 1/2 + 1/6 + 1/12 + … + 1/240 + 1/272`
`= 1 + 1/(1 . 2) + 1/(2 . 3) + ..+ 1/(15 . 16) + 1/(16 . 17)`
`= 1 + (2 – 1)/(1 . 2) + (3 – 2)/(2 . 3) + ..+ (16 – 15)/(15 . 16) + (17 – 16)/(16 . 17)`
`= 1 + 1 – 1/2 + 1/2 – 1/3 + 1/3 – ….+ 1/15 – 1/16 + 1/16 – 1/17`
`= 1 + 1 – 1/17`
`= 2 – 1/17`
`= 34/17 – 1/17`
`= 33/17`
`1+1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132+1/156+1/182+1/210+1/240+1/272`
=`1+1/1.2+1/2.3+1/3.4+1/4.5+……+1/15.16+1/16.17`
=`1+(1-1/2+1/2-1/3+1/3-1/4+…..+1/15-1/16+1/16-1/17)`
=`1+1-1/17`
=`2-1/17`
=`33/17`