(2)①22.5

② Method 1:

∫aa 1 = a 1 a2 = a2 a3 = 1，a 1a2⊥a2a3,∴a 1a3=,aa3= 1+.

∴a 1a2∥a3a4. ∵a2a3⊥a3a4 in the same way: A3A4∥A5A6, ∴ A = ∠ AA2A 1 = ∠ AA4A3 =

∴aa3=a3a4,aa5=a5a6,∴a2= a3 a4 = aa3 = 1+，a3=AA3+A3A5=a2+A3A5。 A3A5 = a2，

∴a3=A5A6=AA5=a2+a2=(+ 1)2.

Method 2:

∫aa 1 = a 1 a2 = a2 a3 = 1，a 1a2⊥a2a3,∴a 1a3=,aa3= 1+.

∴a 1a2∥a3a4. ∵a2a3⊥a3a4 in the same way: A3A4∥A5A6, ∴ A = ∠ AA2A 1 = ∠ AA4A3 =

∴a2=A3A4=AA3= 1+, and ∵ A2A3A4 = ∠ A4A5A6 = 90, ∠A2A4A3=∠A4A6A5, ∴△ A2A3A4.

∴,∴a3==(+ 1)2.

an=(+ 1)n- 1。

(3)

(4) From the meaning of the question, ∴ 15 < ≤ 18.

Don't doubt, I'm copying! Anyway, I didn't succeed. I am curious. Did the landlord do it before? )