4)Chứng tỏ rằng : 11/15<1/21+1/22+1/23+......+1/59+1/60<3/2 5) Chứng tỏ rằng : 3<1+1/2+1/3+1/4+.....+1/63<6 15/08/2021 Bởi Alexandra 4)Chứng tỏ rằng : 11/15<1/21+1/22+1/23+......+1/59+1/60<3/2 5) Chứng tỏ rằng : 3<1+1/2+1/3+1/4+.....+1/63<6
Đáp án: 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 (1) Lại có: 1/21<1/20, 1/22<1/20,…,1/40<1/20 =>1/21+1/22+…+1/40<1/20+1/20+…+1/20=1/20.20=1 1/41<1/40, 1/42<1/40,…,1/60<1/40 =>1/41+1/42+…+1/60<1/40+1/40+…+1/40=1/40.20=1/2 =>1/21+1/22+…+1/60<1+1/2=3/2 =>A<3/2 (2) Từ (1) và (2) =>11/15<A<3/2 =>11/15<1/21+1/22+…+1/59+1/60<3/2 mik chỉ trả lời được câu 4 thôi Bình luận
Đáp án:
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 (1)
Lại có: 1/21<1/20, 1/22<1/20,…,1/40<1/20
=>1/21+1/22+…+1/40<1/20+1/20+…+1/20=1/20.20=1
1/41<1/40, 1/42<1/40,…,1/60<1/40
=>1/41+1/42+…+1/60<1/40+1/40+…+1/40=1/40.20=1/2
=>1/21+1/22+…+1/60<1+1/2=3/2
=>A<3/2 (2)
Từ (1) và (2)
=>11/15<A<3/2
=>11/15<1/21+1/22+…+1/59+1/60<3/2
mik chỉ trả lời được câu 4 thôi