设正项数列an的前n项和是sn,向量a=(sn,1),向量b=(an+1,2),n

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(1)
a=(√Sn,1),b=(an +1,2)
a//b
√Sn/(an +1)=1/2
2√Sn = an + 1
4Sn = (an + 1)^2
n=1,
(a1)^2-2a1=1=0
a1=1
an = Sn-S(n-1)
4an = (an + 1)^2 - (a(n-1) + 1)^2
(an)^2- [a(n-1)]^2 - 2[an + a(n-1)]=0
[an + a(n-1)].[an - a(n-1)-2]=0
an - a(n-1)-2=0
an-a(n-1) =2
an-a1=2(n-1)
an = 2n-1
(2)
bn= an/(an +t)
b1,b2,bm成等差数列
b1+bm = 2b2
a1/(a1 +t) + am/(am +t) = 2[a2/(a2 +t)]
1/(1 +t) + (2m-1)/(2m-1 +t) = 2[3/(3 +t)]
2- t/(1+t) - t/(2m-1 +t) = 2 - 2t/(3 +t)
1/(1+t) + 1/(2m-1 +t) = 2/(3+t)
2(1+t)(2m-1+t) = 2(m +t)(3+t)
t^2+2mt+(2m-1) = t^2+(m+3)t+3m
(m-3)t = m+1
t = (m+1)/(m-3)
m=4
t= 5

1年前

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