If n is a positive integer, then (- 1) 2n=______ ，（-1）2n+1=______ ．

If n is a positive integer, then (- 1) 2n=______ ，（-1）2n+1=______ ．

∵ n is a positive integer, ∵ 2n must be even, 2n + 1 must be odd, ∵ - 1) 2n = 1, (- 1) 2n + 1 = - 1, so the answer is 1, - 1

(2 + 1) (2 ^ 2 + 1) (2 ^ 4 + 1)... (2 ^ 2n + 1) + 1 (n is a positive integer) calculation

（2+1）（2^2+1）（2^4+1）...（2^2n+1）+1
=1*（2+1）（2^2+1）（2^4+1）...（2^2n+1）+1
=(2-1)(2+1)(2^2+1)(2^4+1).(2^2n+)+1
=(2^2-1)(2^2+1)(2^4+1).(2^2n+1)+1
=(2^4-1)(2^4+1).(2^2n+1)+1
=(2^8-1).(2^2n+1)+1
=(2^2n-1)(2^2n+1)+1
=2^4n-1+1
=2^4n

The result of calculating (- 2) 2n + 1 + 2 · (- 2) 2n (n is a positive integer) is______ ．

(- 2) 2n + 1 + 2 · (- 2) 2n = - 22n + 1 + 2 × 22n = - 22n + 1 + 22n + 1 = 0