Cho A = 1/4² + 1/6² +1/8² +…+1/160²
Chứng minh:
1/8
Cho A = 1/4² + 1/6² +1/8² +…+1/160²
Chứng minh:
1/8
By Alexandra
By Alexandra
Ta có:
1/4^2+1/6^2+1/8^2+……+1/160^2
=1/4(1/2^2+1/3^2+1/4^2+………+1/80^2)
Ta có
1/2^2>1/2.3
1/3^2>1/3.4
……..
1/80^2>1/80.81
A>1/4(1/2.3+1/3.4+1/4.5+…….+1/80.81)=1/4(1/2-1/3+1/3-1/4+……+1/80-1/81)=1/4(1/2-1/81)=1/8-1/324>1/8
Vậy A>1/8
Ta lại có
1/2^2=1/4
1/3^2<1/2.3
…….
1/80^2<1/79.80
A<1/4(1/4+1/2.3+…….+1/79.80)=1/4(1/4+1/2-1/3+……+1/79-1/80)=1/4(1/4+1/2-1/80) =1/4(20/80+40/80-1/80)=(1/4).(59/80)=59/320<60/320=3/16
Vậy A<3/16