(2+1)(2^2+1)(2^4+1)(2^8+1)（2^16+1）－2^32

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(2+1)(2^2+1)(2^4+1)(2^8+1)（2^16+1）－2^32
(2+1)(2^2+1)(2^4+1)(2^8+1)（2^16+1）－2^32

(2+1)(2^2+1)(2^4+1)(2^8+1)（2^16+1）－2^32
2^32 -1 =(2^16+1)(2^16-1)
=(2^16+1)(2^8+1)(2^8-1)
.
=(2^16+1)(2^8+1)(2^4+1)(2^2+1)(2+1)(2-1)
=(2^16+1)(2^8+1)(2^4+1)(2^2+1)(2+1)
所以原式 = -1

先在前面乘以（2-1），然后连续运用平方差公式。
(2+1)(2^2+1)(2^4+1)(2^8+1)（2^16+1）－2^32
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)（2^16+1）－2^32
=(2²-1)(2²+1)(2^4+1)(2^8+1)（2^16+1）－2^32
=(2^4-1)(2^4+1)(2^8...

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先在前面乘以（2-1），然后连续运用平方差公式。
(2+1)(2^2+1)(2^4+1)(2^8+1)（2^16+1）－2^32
=(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)（2^16+1）－2^32
=(2²-1)(2²+1)(2^4+1)(2^8+1)（2^16+1）－2^32
=(2^4-1)(2^4+1)(2^8+1)（2^16+1）－2^32
=(2^8-1)(2^8+1)(2^16+1)-2^32
=(2^16-1)(2^16+1)-2^32
=2^32-1-2^32
=-1

收起

1/2,1/4, (1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2009^2), (2+1)({2}^{2}+1)({2}^{4}+1)({2}^{8}+1).({2}^{64}+1)+1 巧算((2^1+1)(2^2+1)(2^4+1)(2^8+1)+1)/2^15 计算(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1 计算:(2+1)(2^2+1)(2^4+1)(2^8+1)-2^16.计算：(2+1)(2^2+1)(2^4+1)(2^8+1)-2^16. [(1+2^-(1/32)]*[(1+2^-(1/16)]*[(1+2^-(1/8)]*[(1+2^-(1/4)]*[(1+2^-(1/2)] (1-1/2^2)*(1-1/3^2)*(1-1/4^2)*.*(1-1/2002^2)*(1-1/2003^2) (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16), 1,2,4,4,1,( ) (2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1 (2^2+1)*(2^4+1)*(2^8+1)*(2^16+1)*(2^32+1） (2+1)(2-1)(2^2+1)(2^4+1).(2^8+1)化简 (1+2)*(1+2^2)*(1+2^4)*(1+2^8)*(1+2^16) 化简(1+2)(1+2^2)(1+2^4)(1+2^8)(1+2^16) 化简(2+1)(2^2+1)(2^4+1)(2^8+1)…(2^256+1) (2-1)(2+1)(2^2+1)(2^4)...(2^64+1)+1=? (2+1)(2^2+1)(2^4+1)(2^8+1)……(2^1024+1)