tính nhanh (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+…+(1/1+2+3+..+99) 30/10/2021 Bởi Allison tính nhanh (1/1+2)+(1/1+2+3)+(1/1+2+3+4)+…+(1/1+2+3+..+99)
(1/1+2)+(1/1+2+3)+(1/1+2+3+4)+…+(1/1+2+3+..+99) = 1/3+ 1/6+ 1/10+…+ 1/4950 = 2. ( 1/6+ 1/12+ 1/20+…+ 1/9900] = 2. ( 1/2.3 + 1/3.4+….+1/99.100] = 2. ( 1/2- 1/3+ 1/3- 1/4+…+ 1/99- 1/100] = 2. ( 1/2- 1/100] = 2. 49/100 = 49/50 Nên A= 49/50 Học tốt nhé! Bình luận
`1/(1 + 2) + 1/(1 + 2 + 3) + 1/(1 + 2 + 3 + 4) + ….. + 1/(1 + 2 + 3 + …. + 99)` `= 1/3 + 1/6 + 1/10 + …. + 1/4950` `= 2 . (1/6 + 1/12 + 1/20 + … + 1/9900)` `= 2 . (1/(2.3) + 1/(3.4) + 1/(4.5) + …. 1/(99.100))` `= 2 . (1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + …. + 1/99 – 1/100)` `= 2 . (1/2 – 1/100)` `= 2 . 49/100` `= 49/50` Bình luận
(1/1+2)+(1/1+2+3)+(1/1+2+3+4)+…+(1/1+2+3+..+99)
= 1/3+ 1/6+ 1/10+…+ 1/4950
= 2. ( 1/6+ 1/12+ 1/20+…+ 1/9900]
= 2. ( 1/2.3 + 1/3.4+….+1/99.100]
= 2. ( 1/2- 1/3+ 1/3- 1/4+…+ 1/99- 1/100]
= 2. ( 1/2- 1/100]
= 2. 49/100
= 49/50
Nên A= 49/50
Học tốt nhé!
`1/(1 + 2) + 1/(1 + 2 + 3) + 1/(1 + 2 + 3 + 4) + ….. + 1/(1 + 2 + 3 + …. + 99)`
`= 1/3 + 1/6 + 1/10 + …. + 1/4950`
`= 2 . (1/6 + 1/12 + 1/20 + … + 1/9900)`
`= 2 . (1/(2.3) + 1/(3.4) + 1/(4.5) + …. 1/(99.100))`
`= 2 . (1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + …. + 1/99 – 1/100)`
`= 2 . (1/2 – 1/100)`
`= 2 . 49/100`
`= 49/50`