An=(2的n次方-1)/2的n次方,令Bn=(2-n)/(An-1)对于任意n都有BN=1/4*t小或等于t的平方,求实数t的取值范围

An=(2^n-1)/2^n=1-1/2^n =1-0.5^nBn=(2-n)/(An-1)=(2-n)/(1-1/2^n-1)=(2-n)/(-1/2^n)=(n-2)*2^nt/4≤t² t(t-1/4)≥0 t≥1/4或t≤0Bn=(n-2)*2^n=t/4 t=(n-2)*2^(n+2)t′=[1+(x-2)㏑2]*2^(mn+2) x>2-1/㏑2 时t′...An=(2的n次方-1)/2的n次方，令Bn=(2-n)/(An-1)对于任意n都有Bn+1/4*t小或等于t的平方,求实数t的取值范围An=(2^n-1)/2^n=1-1/2^n =1-0.5^nBn=(2-n)/(An-1)=(2-n)/(1-1/2^n-1)=(2-n)/(-1/2^n)=(n-2)*2^nBn+t/4= (n-2)*2^n +t/4 ≤t²t²-t/4≥BnBn=(n-2)*2^n Bn′=[1+(n-2)㏑2]*2^nn>2-1/㏑2 时Bn′0n=2-1/㏑2 时Bn′=0所以Bn(max)=(2-1/ln2-2)*2^(2-1/ln2)= (-1/ln2)*(2^2)/[2^(1/ln2)]=-4/[ln2*2(1/ln2)]所以t²-t/4≥ -4/[ln2*2(1/ln2)]