Toán Chứng minh rằng:A=1/2+1/2^2+1/2^3+1/2^4+1/2^5 <1 28/10/2021 By Alaia Chứng minh rằng:A=1/2+1/2^2+1/2^3+1/2^4+1/2^5 <1
$A = \dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+\dfrac{1}{2^5}$ $=1-\dfrac{1}{2^5} <1$ Trả lời
`A=1/2+1/(2^2)+1/(2^3)+1/(2^4)+1/(2^5) ` ⇒`2A=1+1/2+1/(2^2)+1/(2^3)+1/(2^4)` ⇒`2A-A=1+1/2+1/(2^2)+1/(2^3)+1/(2^4)-1/2-1/(2^2)-1/(2^3)-1/(2^4)-1/(2^5)` ⇔`A=1-1/(2^5)` ⇔`A<1(Đpcm)` Trả lời
$A = \dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+\dfrac{1}{2^5}$
$=1-\dfrac{1}{2^5} <1$
`A=1/2+1/(2^2)+1/(2^3)+1/(2^4)+1/(2^5) `
⇒`2A=1+1/2+1/(2^2)+1/(2^3)+1/(2^4)`
⇒`2A-A=1+1/2+1/(2^2)+1/(2^3)+1/(2^4)-1/2-1/(2^2)-1/(2^3)-1/(2^4)-1/(2^5)`
⇔`A=1-1/(2^5)`
⇔`A<1(Đpcm)`