设数列An是公差为d的等差数列,A3+A5=2,S20=A1+A2+.+A20=150,Bn=2^(An-2A(n+1)),.1)求A1,d的值2)求证:Bn是等比数列,并求Bn3)设k为正整数,且满足lim(BkBk+1 + Bk+1Bk+2 +……+ BnBn+1)=1/96,求k的值

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设数列An是公差为d的等差数列,A3+A5=2,S20=A1+A2+.+A20=150,Bn=2^(An-2A(n+1)),.1)求A1,d的值2)求证:Bn是等比数列,并求Bn3)设k为正整数,且满足lim(BkBk+1 + Bk+1Bk+2 +……+ BnBn+1)=1/96,求k的值

设数列An是公差为d的等差数列,A3+A5=2,S20=A1+A2+.+A20=150,Bn=2^(An-2A(n+1)),.1)求A1,d的值2)求证:Bn是等比数列,并求Bn3)设k为正整数,且满足lim(BkBk+1 + Bk+1Bk+2 +……+ BnBn+1)=1/96,求k的值
设数列An是公差为d的等差数列,A3+A5=2,S20=A1+A2+.+A20=150,Bn=2^(An-2A(n+1)),.
1)求A1,d的值
2)求证:Bn是等比数列,并求Bn
3)设k为正整数,且满足lim(BkBk+1 + Bk+1Bk+2 +……+ BnBn+1)=1/96,求k的值

设数列An是公差为d的等差数列,A3+A5=2,S20=A1+A2+.+A20=150,Bn=2^(An-2A(n+1)),.1)求A1,d的值2)求证:Bn是等比数列,并求Bn3)设k为正整数,且满足lim(BkBk+1 + Bk+1Bk+2 +……+ BnBn+1)=1/96,求k的值
(1)a3+a5=2a4=2
a4=1
s20=(a1+a20)*20/2=10(a1+a20)=150
a1+a20=15=a4+a17
a17=14
d=(a17-a4)/13=1
a1=a4-3d=-2
an=-2+(n-1)=n-3
(2)bn=2^(n-3-2(n-2))=2^(1-n)
bn/b(n-1)=2^(1-n)/2^(2-n)=1/2=常数
得证
(3)可设tn=bn*b(n+1)=2^(1-2n)
lim(Xn)=lim(tk+t(k+1)+t(k+2)+……)=2^(1-2k)/(1-1/4)=1/96
k=4
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