Toán Chứng tỏ rằng 11/15<1/21+1/22+1/23+...+1/63 Ko cOP MẠNG NHÉ 23/10/2021 By Josie Chứng tỏ rằng 11/15<1/21+1/22+1/23+...+1/63 Ko cOP MẠNG NHÉ
Đáp án: Đây là lần thứ 3 mik làm ^^ Giải thích các bước giải: Đặt `A=1/21+1/22+…+1/60=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/60)` Ta có : `1/21>1/40, 1/22>1/40,…, 1/39>1/40` `⇒ 1/21+1/226+…+1/40>1/40+1/40+…+1/40=1/40.20 = 1/2` `1/41>1/60, 1/42>1/60,…,1/59>1/60` `⇒ 1/41+1/42+…+1/60>1/60+1/60+…+1/60=1/60.20 = 1/3` `⇒ 1/21+1/22+…+1/60>1/2+1/3=5/6 > 11/15` `⇒ A >11/15` `hay` `11/15 < A` Trả lời
Đặt `B=1/21+1/22+…+1/60=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/60)` Ta có : `1/21>1/40, 1/22>1/40,…, 1/39>1/40` `⇒ 1/21+1/226+…+1/40>1/40+1/40+…+1/40=1/40.20 = 1/2` `1/41>1/60, 1/42>1/60,…,1/59>1/60` `⇒ 1/41+1/42+…+1/60>1/60+1/60+…+1/60=1/60.20 = 1/3` `⇒ 1/21+1/22+…+1/60>1/2+1/3=5/6 > 11/15` `⇒ A >11/15` `hay` `11/15 < A` Trả lời
Đáp án:
Đây là lần thứ 3 mik làm ^^
Giải thích các bước giải:
Đặt `A=1/21+1/22+…+1/60=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/60)`
Ta có : `1/21>1/40, 1/22>1/40,…, 1/39>1/40`
`⇒ 1/21+1/226+…+1/40>1/40+1/40+…+1/40=1/40.20 = 1/2`
`1/41>1/60, 1/42>1/60,…,1/59>1/60`
`⇒ 1/41+1/42+…+1/60>1/60+1/60+…+1/60=1/60.20 = 1/3`
`⇒ 1/21+1/22+…+1/60>1/2+1/3=5/6 > 11/15`
`⇒ A >11/15` `hay` `11/15 < A`
Đặt `B=1/21+1/22+…+1/60=(1/21+1/22+…+1/40)+(1/41+1/42+…+1/60)`
Ta có : `1/21>1/40, 1/22>1/40,…, 1/39>1/40`
`⇒ 1/21+1/226+…+1/40>1/40+1/40+…+1/40=1/40.20 = 1/2`
`1/41>1/60, 1/42>1/60,…,1/59>1/60`
`⇒ 1/41+1/42+…+1/60>1/60+1/60+…+1/60=1/60.20 = 1/3`
`⇒ 1/21+1/22+…+1/60>1/2+1/3=5/6 > 11/15`
`⇒ A >11/15` `hay` `11/15 < A`