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Toán Lớp 6: Cho A =1/2^2+1/2^4+1/2^6+…+1/2^100 Chứng minh A<1/3

Home/ Toán Lớp 6: Cho A =1/2^2+1/2^4+1/2^6+…+1/2^100 Chứng minh A<1/3

Toán Lớp 6: Cho A =1/2^2+1/2^4+1/2^6+…+1/2^100 Chứng minh A<1/3

Cẩm Thúy Tháng Hai 2, 2023 Toán học 1 Comment 0 views

Toán Lớp 6: Cho A =1/2^2+1/2^4+1/2^6+…+1/2^100
Chứng minh A<1/3

Comments ( 1 )

mytamhoang
2 Tháng Hai, 2023 at 9:48 sáng

Reply

A=\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+…+\frac{1}{2^100}

frac{1}{2^2}A=\frac{1}{2^4}+\frac{1}{2^6}+\frac{1}{2^8}…+\frac{1}{2^102}

=>A-frac{1}{2^2}A=(\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+…+\frac{1}{2^100})-(\frac{1}{2^4}+\frac{1}{2^6}+\frac{1}{2^8}…+\frac{1}{2^102})

=>A-frac{1}{2^2}A=\frac{1}{2^2}-\frac{1}{2^102}

=>3/4 A=1/4-\frac{1}{2^102}

=>3/4 A<1/4

=>A<1/4:3/4

=>A<1/3

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