tính giá trị biểu thức: A= 1+1/3+1/6+1/10+1/15+…+1/120 13/08/2021 Bởi Valentina tính giá trị biểu thức: A= 1+1/3+1/6+1/10+1/15+…+1/120
Đáp án: `15/8` Giải thích các bước giải: `1+1/3+1/6+1/10+1/15+…+1/120` `=2/2+2/6+2/12+2/20+2/30+…+2/240` `=2(1-1/6+1/12+1/20+1/30+…+1/240)` `=2(1-1/2.3“+1/3.4“+1/4.5“+1/5.6“+…+1/15.16)` `=2(1-1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+…+1/15-1/16)` `=2(1-1/16)` `=2.` `15/16` `=15/8` Bình luận
` 1 + 1/3 + 1/6 + 1/10 + 1/15 + … + 1/120` `= 2/2 + 2/6 + 2/12 + 2/20 + 2/30 + … + 2/240` `= 2/1.2 + 2/2.3 + 2/3.4 + 2/4.5 + 2/5.6 +… + 2/15.16` `= 2 . (1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/15 – 1/16)` `= 2 . ( 1 – 1/16 )` `= 2 . 15/16` `= 15/8` Bình luận
Đáp án: `15/8`
Giải thích các bước giải:
`1+1/3+1/6+1/10+1/15+…+1/120`
`=2/2+2/6+2/12+2/20+2/30+…+2/240` `=2(1-1/6+1/12+1/20+1/30+…+1/240)`
`=2(1-1/2.3“+1/3.4“+1/4.5“+1/5.6“+…+1/15.16)` `=2(1-1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+…+1/15-1/16)` `=2(1-1/16)`
`=2.` `15/16`
`=15/8`
` 1 + 1/3 + 1/6 + 1/10 + 1/15 + … + 1/120`
`= 2/2 + 2/6 + 2/12 + 2/20 + 2/30 + … + 2/240`
`= 2/1.2 + 2/2.3 + 2/3.4 + 2/4.5 + 2/5.6 +… + 2/15.16`
`= 2 . (1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/15 – 1/16)`
`= 2 . ( 1 – 1/16 )`
`= 2 . 15/16`
`= 15/8`