Toán Lớp 6: Cho A = 1/2×2 + 1/3×3 + 1/4×4 + … +1/2020×2020. So sánh A với 1
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 6: Cho A = 1/2×2 + 1/3×3 + 1/4×4 + … +1/2020×2020. So sánh A với 1
Comments ( 2 )
1/2.2<1/1.2
1/3.3<1/2.3
…
1/2020.2020<1/2019.2020
Nên:
A<1/1.2+1/2.3+1/3.4+….+1/2019.2020
A<(2-1)/1.2+(3-2)/2.3+(4-3)/3.4+…+(2020-2019)/2019.2020
A<1/1.2-2/1.2+2/2.3-3/2.3+3/3.4+4/3.4+…+2020/2019.2020-2019/2019.2020
A<1-1/2+1/2-1/3+….+1/2019-1/2020
A<1-1/2020
Vì 1-1/2020< 1
Nên: A <1 $\text{(Điều phải chứng minh)}$