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](/uploads/image/z/2707697-65-7.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97An%E6%98%AF%E5%85%AC%E5%B7%AE%E4%B8%BAd%E7%9A%84%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2CA3%2BA5%3D2%2CS20%3DA1%2BA2%2B.%2BA20%3D150%2CBn%3D2%5E%28An-2A%28n%2B1%29%29%2C.1%EF%BC%89%E6%B1%82A1%2Cd%E7%9A%84%E5%80%BC2%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9ABn%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%B9%B6%E6%B1%82Bn3%EF%BC%89%E8%AE%BEk%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E4%B8%94%E6%BB%A1%E8%B6%B3lim%28BkBk%2B1+%2B+Bk%2B1Bk%2B2+%2B%E2%80%A6%E2%80%A6%2B+BnBn%2B1%29%3D1%2F96%2C%E6%B1%82k%E7%9A%84%E5%80%BC)
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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