解题须知:
(a + b)(a - b) = a^2 - b^2
(2^a + 1)(2^a - 1) = (2^a)^2 - 1 = 2^2a - 1
(2^(2^a) + 1)(2^(2^a) - 1) = 2^(2 * 2^a) - 1 = 2^(2^(a +1)) - 1
2^(2^0) - 1 = 1
(F0)(F1)...(Fn-1) + 2
= (1)(F0)(F1)...(Fn-1) + 2
= (2^(2^0) - 1) (2^(2^0) + 1) (2^(2^1) + 1) ...(2^(2^(n-1)) + 1) + 2
= (2^(2^1) - 1) (2^(2^1) + 1) (2^(2^2) + 1) ...(2^(2^(n-1)) + 1) + 2
= (2^(2^2) - 1) (2^(2^2) + 1) (2^(2^3) + 1) ...(2^(2^(n-1)) + 1) + 2
= ...
= (2^(2^n) - 1) + 2
= 2^(2^n) + 1
= Fn
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