Cho A = 1/4² + 1/6² +1/8² +…+1/160²
Chứng minh:
1/8 { "@context": "https://schema.org", "@type": "QAPage", "mainEntity": { "@type": "Question", "name": " Cho A = 1/4² + 1/6² +1/8² +...+1/160²
Chứng minh:
1/8
0 bình luận về “Cho A = 1/4² + 1/6² +1/8² +…+1/160²
Chứng minh:
1/8<A<3/16
Nhanh nha^^ mình vote 5 sao lun”
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
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