数列中,a1=1,an+1*根号an=8,求anan+1是An+1 即an后一项
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数列中,a1=1,an+1*根号an=8,求anan+1是An+1 即an后一项
数列中,a1=1,an+1*根号an=8,求an
an+1是An+1 即an后一项
数列中,a1=1,an+1*根号an=8,求anan+1是An+1 即an后一项
a(n+1)·√an=8
a1=1>0,假设当n=k(k∈N+)时,ak>0,则
a(k+1)=8/√ak>0
k为任意正整数,因此,对于任意正整数n,an恒>0
log2[a(n+1)√an]=log2(8)
log2[a(n+1)]+(1/2)log2(an)=3
log2[a(n+1)] -2=-(1/2)log2(an) +1=(-1/2)[log2(an) -2]
[ log2[a(n+1)] -2]/[log2(an) -2]=-1/2,为定值
log2(a1) -2=log2(1) -2=0-2=-2
数列{log2(an) -2}是以-2为首项,-1/2为公比的等比数列
log2(an) -2=(-2)(-1/2)^(n-1)=(-1/2)^(n-2)
log2(an)=2 -(-1/2)^(n-2)
an=2^[2-(-1/2)^(n-2)]
a(n+1)*√an=8
lg[a(n+1)*√an]=lg(8)
lg[a(n+1)+1/2lg(an)=lg(8)
lg[a(n+1)=-1/2[lg(an)+3lg(2)]
lg[a(n+1)-2lg(2)=-1/2[lg(an)-2lg(2)]
{lg(an)-2lg(2)}为等比,公比=-1/2,首项=lg(a1)-2lg(2)=-2lg(2)
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a(n+1)*√an=8
lg[a(n+1)*√an]=lg(8)
lg[a(n+1)+1/2lg(an)=lg(8)
lg[a(n+1)=-1/2[lg(an)+3lg(2)]
lg[a(n+1)-2lg(2)=-1/2[lg(an)-2lg(2)]
{lg(an)-2lg(2)}为等比,公比=-1/2,首项=lg(a1)-2lg(2)=-2lg(2)
lg(an)-2lg(2)=-2lg(2)*(-1/2)^(n-1)
lg(an)=2lg(2)[1-(-1/2)^(n-1)]
lg(an)=lg(2)^[2(1-(-1/2)^(n-1)]
an=(4)^[1-(-1/2)^(n-1)]
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