Đáp án + Giải thích các bước giải:
` 17. `
`5/(1xx4) + 5/(4xx7) + ... + 5/(91xx94)`
`= 5 . 1/3. (1 - 1/4 + 1/4 - 1/7 + ... + 1/91 - 1/94)`
`= 5/3. (1 - 1/94)`
`= 5/3. (94/94 + (-1)/94)`
`= 5/3. 93/94`
`= 155/94`
`18.`
`5/(1xx10) + 5/(10xx19) + ... + 5/(91xx100)`
`= 5 . 1/9. (1 - 1/10 + 1/10 - 1/19 + ... + 1/91 - 1/100)`
`= 5/9. (1 - 1/100)`
`= 5/9. (100/100 + (-1)/100)`
`= 5/9. 99/100`
`= 11/20`
Bài `4:`
`1,` `B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30`
` B = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6`
`B = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6`
` B = 1 - 1/6`
` B = 6/6 + (-1)/6`
` B = 5/6`
`2,` `B = 1/15 + 1/35 + 1/63 + 1/99 + 1/143`
` B = 1/3.5 + 1/5.7 + 1/7.9 + 1/9.11 + 1/11.13`
`B = 1/2. (1/3 - 1/5 + 1/5 - 1/7 + ... + 1/11 - 1/13)`
` B = 1/2. (1/3 - 1/13)`
` B = 1/2. (13/39 + (-3)/39)`
` B = 1/2. 10/39`
`B = 5/39`
`3,` `B = 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56`
` B = 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8`
` B = 1/2 - 1/3 + 1/3 - 1/4 + ... 1/7 - 1/8`
`B = 1/2 - 1/8`
` B = 4/8 + (-1)/8`
` B = 3/8`
`4, ` `B = 1/2 + 1/14 + 1/35 + 1/65 + 1/104 + 1/152`
`=> B = 2/4 + 2/28 + 2/70 + 2/130 + 2/208 + 1/304`
`B = 2/1.4 + 2/4.7 + 2/7.10 + 2/10.13 + 2/13.16 + 2/16.19`
` B = 2. 1/3. (1 - 1/4 + 1/4 - 1/7 + ... + 1/16 - 1/19)`
` B = 2/3. (1 - 1/19)`
`B = 2/3. (19/19 + (-1)/19)`
` B = 2/3. 18/19`
` B = 12/19`
`5,` `B = 1/7 + 1/91 + 1/247 + 1/475 + 1/755 + 1/1147`
`B = 1/1.7 + 1/7.13 + 1/13.19 + 1/19.25 + 1/25.31 + 1/31.37`
`B = 1/6. (1 - 1/7 + 1/7 - 1/13 + ... + 1/31 - 1/37)`
`B = 1/6. (1 - 1/37)`
`B = 1/6. (37/37 + (-1)/37)`
`B = 1/6 . 36/37`
`B = 6/37`
`6,` `2/6 + 2/66 + 2/176 + ... + 2/51.56`
`= 2/1.6 + 2/6.11 + 2/11.16 + ... + 2/51.56`
`= 2 . 1/5 . (1 - 1/6 + 1/6 - 1/11 + ... + 1/51 - 1/56)`
`= 2/5 . (1 - 1/56)`
`= 2/5 . (56/56 + (-1)/56)`
`= 2/5 . 55/56`
`= 11/28`
