If the positive number k is the median of the real numbers 2a and 2B, and the root K is the median of a and B, then the value range of K is?

If the positive number k is the median of the real numbers 2a and 2B, and the root K is the median of a and B, then the value range of K is?

Easy to know
K = a + B, k = AB, a + B = AB, and a, B have the same sign, a and B are not 1, not 0
b=a/(a-1),
k=ab=a^2/(a-1)=(u+1)^2/u=2+u+1/u,u=a-1>0
So k > = 4

Delete all the complete square numbers in the positive integer sequence 1,2,3. To get a new sequence, find the 2007 item of the sequence?

The square of 45 is 2025, minus 1 ^ 2,2 ^ 2,3 ^ 2,4 ^ 2 The 45 numbers, 1980 is not enough. Similarly, 46 * 46 minus 46 is 2070, which is larger than 2007. So 2026 is the 1980, 2027 is the 1982, so add it back directly, and the 2007 is 2052

The sequence {an} satisfies an + 1 = 1 / (2-An),
A1, n (n > 2) denotes an =?

(an+1)-1=1/[2-an]-1=(an-1)/(2-an),
Let BN = an-1, then B (n + 1) = BN / (1-bn),
1/(bn+1)=1/bn-1,
1/(bn+1)-1/bn=-1,
So the first term of {1 / BN} is an arithmetic sequence with 1 / B1 = 1 / (A-1) and tolerance of - 1,
1/bn=1/(a-1)-(n-1),
bn=(a-1)/[n(1-a)+a],
So an = BN + 1 = [(n-1) (1-A)] / [n (1-A) + a]