Toán A=½²+½⁴+½⁶+½⁸+…+½¹⁰⁰ . Chứng minh rằng A<⅓ 27/11/2021 By Delilah A=½²+½⁴+½⁶+½⁸+…+½¹⁰⁰ . Chứng minh rằng A<⅓
Tham khảo `A=\frac{1}{2^2}+\frac{1}{2^4}+..+\frac{1}{2^{100}}` `⇒2^2A=1+\frac{1}{2^2}+..+\frac{1}{2^{98}}` `⇒4A-A=1+\frac{1}{2^2}+..+\frac{1}{2^{98}}-(\frac{1}{2^2}+\frac{1}{2^4}+..+\frac{1}{2^{100}})` `⇒3A=1-\frac{1}{2^{100}}` Vì `1-\frac{1}{2^{100}}<1` `⇒3A<1` `⇒A<\frac{1}{3}` Trả lời
Tham khảo
`A=\frac{1}{2^2}+\frac{1}{2^4}+..+\frac{1}{2^{100}}`
`⇒2^2A=1+\frac{1}{2^2}+..+\frac{1}{2^{98}}`
`⇒4A-A=1+\frac{1}{2^2}+..+\frac{1}{2^{98}}-(\frac{1}{2^2}+\frac{1}{2^4}+..+\frac{1}{2^{100}})`
`⇒3A=1-\frac{1}{2^{100}}`
Vì `1-\frac{1}{2^{100}}<1`
`⇒3A<1`
`⇒A<\frac{1}{3}`
@py
Bài làm :