(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1

来源：学生作业帮助网 编辑：作业帮 时间：2024/08/27 07:08:38
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
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(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),
题没有打完
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1

(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),题没有打完(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)+1
=(2²-1) (2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),/3+1
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1),/3+1
=...
=(2^128-1)/3 +1
先乘以(2²-1),再除以3,保证相等
然后反复应用平方差公式

(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=（2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1)
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1)
=...
=(2^128-1)/3

[(2^2-1)× (2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1]/(2^2-1)
=[(2^4-1)2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^16-1)(2^16+1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^32-1)(2^32+1)(2^64+1)]/(2^2-1)
=[(2^64-1)(2^64+1)]/(2^2-1)
=(2^128-1)/3

(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=（2^2-1）(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1）
= (2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1）
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)/（2^2-1）
=………………
=（2^128-1）/（2^2-1）
=1.13^38(或=（2^128-1）/3)

比如用(2^2-1)去乘(2^2+1)　用(2^4-1)去乘(2^4+1)…以此类推,再除掉所乘的数.原理一样,但更容易做(个人认为)

(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)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16), 计算1/(1+2)+2/(1+2^2)+4/(1+2^4)+8/(1+2^8)+16/(1+2^16) (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)(2^2+1)(2^4+1)(2^8+1)……(2^1024+1) (2+1)(2^2+1)(2^4+1)(2^8+1).(2^2048+1)=? 初中数学题&(1+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+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1 (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^16