计算(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)！
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(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=(2-1)[(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)]
=[(2-1)(2+1)](2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=(2^2-1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=[(2^2-1)(2^2+1)](2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=(2^4-1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
...
=(2^2n -1)(2^2n+1)
=2^(2n+2)-1
=(2-1)[(2+1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)]
=[(2-1)(2+1)](2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=(2^2-1)(2^2+1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=[(2^2-1)(2^2+1)](2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
=(2^4-1)(2^4+1)(2^6+1)(2^8+1)……(2^2n+1)
...
=(2^2n -1)(2^2n+1)
=2^(2n+2)-1
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