chứng tỏ rằng 1+1/2+1/3+1/4+…+1/31+1/32>7/2 28/07/2021 Bởi Claire chứng tỏ rằng 1+1/2+1/3+1/4+…+1/31+1/32>7/2
Đáp án: Đặt `A = 1 + 1/2 + 1/3 + …………..+1/31 + 1/32` Ta có: `1+ 1/2 + 1/3 + 1/4 + ……. + 1/31 + 1/32= (1 + 1/2 + 1/3 + ….. +1/6) + (1/7 + 1/8+ 1/9+ …………+ 1/12) + ……………… + ( 1/25 + 1/26 + 1/27 + 1/28) + (1/29 + 1/30 + 1/31 + 1/32)` `A> (1 +1/2 + 1/3 + 1/4 + 1/5 + 1/6) + (1/12 + 1/12 +…. + 1/12) + …………….. +( 1/28 + 1/28 + 1/28 + 1/28) + (1/32 + 1/32 + 1/32 + 1/32)` ` = 49/20 + 1/2 + 1/3 + 1/4 + 1/7 + 1/8` ` = 3193/840> 2940/840 = 7/2` `⇒ A>7/2` `text{ XIN HAY NHẤT NHA}` @toanisthebest Bình luận
Đáp án:
Đặt `A = 1 + 1/2 + 1/3 + …………..+1/31 + 1/32`
Ta có: `1+ 1/2 + 1/3 + 1/4 + ……. + 1/31 + 1/32= (1 + 1/2 + 1/3 + ….. +1/6) + (1/7 + 1/8+ 1/9+ …………+ 1/12) + ……………… + ( 1/25 + 1/26 + 1/27 + 1/28) + (1/29 + 1/30 + 1/31 + 1/32)`
`A> (1 +1/2 + 1/3 + 1/4 + 1/5 + 1/6) + (1/12 + 1/12 +…. + 1/12) + …………….. +( 1/28 + 1/28 + 1/28 + 1/28) + (1/32 + 1/32 + 1/32 + 1/32)`
` = 49/20 + 1/2 + 1/3 + 1/4 + 1/7 + 1/8`
` = 3193/840> 2940/840 = 7/2`
`⇒ A>7/2`
`text{ XIN HAY NHẤT NHA}`
@toanisthebest