In the sequence {an}, A1 ＞ 0, a3-a2 = 8, and the middle term of A1, A5 is 16 (1) Let BN = log4an, the sum of the first n terms of the sequence {an} be Sn, whether there is a positive integer k such that 1 / S1 + 1 / S2 + 1 / S3 + +1 / Sn ＜ K holds for any n ∈ n * constant? If it exists, find the minimum value of positive integer K. if it does not exist, explain the reason

In the sequence {an}, A1 ＞ 0, a3-a2 = 8, and the middle term of A1, A5 is 16 (1) Let BN = log4an, the sum of the first n terms of the sequence {an} be Sn, whether there is a positive integer k such that 1 / S1 + 1 / S2 + 1 / S3 + +1 / Sn ＜ K holds for any n ∈ n * constant? If it exists, find the minimum value of positive integer K. if it does not exist, explain the reason

(1) The median of A1 and A5 is 16
So A3 = 16 or - 16
If A3 = - 16, then A2 = - 24 is not suitable
So A3 = 16
a2=8
So an = 2 ^ (n + 1)
(2)bn=(n+1)/2
Sn=n(n+3)/4
1/Sn=4/[n(n+3)]=4/3[1/n-1/(n+3)]
So 1 / S1 + 1 / S2 +... + 1 / Sn = 4 / 3 (1-1 / 4) + 4 / 3 (1 / 2-1 / 5) +... + 4 / 3 (1 / n-1 / (n + 3))
=4/3[1+1/2+1/3-1/(n+1)-1/(n+2)-1/(n+3)]

In the known equal ratio sequence an, A1 = 1, A5 = 8a21. Find the general term formula 2 of the sequence an, if bn-an + N, find the first n terms and s of the sequence BN

a5=8a2
a2q³=8a2
q³=8
q=2
N-1 power of an = A1 * 2 = n-1 power of 2
The N-1 power of BN = 2 + n
Sn = (n power of 1-2) / (1-2) + (1 + n) n / 2
=The nth power of 2-1 + 1 / 2n & # 178; + 1 / 2n
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