Cho B = 1/4+1/5+1/6+…+1/19. Hãy chứng minh B < 1. 17/10/2021 Bởi Arianna Cho B = 1/4+1/5+1/6+…+1/19. Hãy chứng minh B < 1.
`text{Ta có : }B = 1/4+1/5+1/6+…+1/19` `toB= 1/4+(1/5+1/6+…+1/8+1/9)+(1/10+1/11+…+1/18+1/19)` `text{Vì } 1/5+1/6+…+1/9 > 1/9+1/9+…+1/9=5/9>1/2 ` `text{Vì }1/10+1/11+…+1/19 > 1/19+1/19+…+1/19=10/19>1/2` `text{Vậy } B > 1/4+1/2+1/2 > 1` Bình luận
Đáp án: Cho B = 1/4+1/5+1/6+…+1/19. Hãy chứng minh B < 1.B= 1/4+(1/5+1/6+…+1/9)+(1/10+1/11+…+1/19)Vì 1/5+1/6+…+1/9 > 1/9+1/9+…+1/9 nên 1/5+1/6+…+1/9 > 5/9 >1/2Vì 1/10+1/11+…+1/19 > 1/19+1/19+…+1/19 nên 1/10+1/11+…+1/19 > 10/19 >1/2⇒ B > 1/4+1/2+1/2 > 1 Chúc bn hok tốt. Bình luận
`text{Ta có : }B = 1/4+1/5+1/6+…+1/19`
`toB= 1/4+(1/5+1/6+…+1/8+1/9)+(1/10+1/11+…+1/18+1/19)`
`text{Vì } 1/5+1/6+…+1/9 > 1/9+1/9+…+1/9=5/9>1/2 `
`text{Vì }1/10+1/11+…+1/19 > 1/19+1/19+…+1/19=10/19>1/2`
`text{Vậy } B > 1/4+1/2+1/2 > 1`
Đáp án:
Cho B = 1/4+1/5+1/6+…+1/19. Hãy chứng minh B < 1.
B= 1/4+(1/5+1/6+…+1/9)+(1/10+1/11+…+1/19)
Vì 1/5+1/6+…+1/9 > 1/9+1/9+…+1/9 nên 1/5+1/6+…+1/9 > 5/9 >1/2
Vì 1/10+1/11+…+1/19 > 1/19+1/19+…+1/19 nên 1/10+1/11+…+1/19 > 10/19 >1/2
⇒ B > 1/4+1/2+1/2 > 1
Chúc bn hok tốt.