Cho A = 1/3 + 1/35 + 1/37 + 1/47 + 1/53 + 1/61 Hãy chứng tỏ A < 1/2 01/08/2021 Bởi Faith Cho A = 1/3 + 1/35 + 1/37 + 1/47 + 1/53 + 1/61 Hãy chứng tỏ A < 1/2
`1/3 + 1/35 + 1/37 + 1/47 + 1/53 + 1/61 < 1/3 + (1/30 + 1/30 ) + (1/45 +1/45 + 1/45)` `1/3 + (1/30 + 1/30) + (1/45 +1/45 + 1/45) = 1/15 + 1/10 + 1/15 = 7/30` `⇔ A < 7/30 < 1/2 (dpcm)` Bình luận
`1/3 + 1/35 + 1/37 + 1/47 + 1/53 + 1/61 < 1/3 + (1/30 + 1/30 ) + (1/45 +1/45 + 1/45)`
`1/3 + (1/30 + 1/30) + (1/45 +1/45 + 1/45) = 1/15 + 1/10 + 1/15 = 7/30`
`⇔ A < 7/30 < 1/2 (dpcm)`