Cho A=1/2+1/2²+1/2³+….+1/2¹⁰⁰
Chứng minh rằng:0
Cho A=1/2+1/2²+1/2³+….+1/2¹⁰⁰
Chứng minh rằng:0
By Clara
By Clara
$A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+…+\dfrac{1}{2^{100}}$
$2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+…+\dfrac{1}{2^{99}}$
$2A-A=(1+\dfrac{1}{2}+\dfrac{1}{2^2}+…+\dfrac{1}{2^{99}})-(\dfrac{1}{2}+\dfrac{1}{2^2}+…+\dfrac{1}{2^{100}})$
$A=1-\dfrac{1}{2^{100}}$
$A=\dfrac{2^{100}-1}{2^{100}}$
Ta thấy $2^{100}-1<2^{100}$
$→A<1$
mà $2^{100}-1>0,2^{100}>0$
$→\dfrac{2^{100}-1}{2^{100}}>0$
Từ hai điều trên
$→0<A<1$