(3+1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)的值

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(3+1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)的值
(3+1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)的值

(3+1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)的值
(3+1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)
=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)/(3-1)
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)……(3^64+1)/2
反复用平方差
=(3^128-1)/2

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

(3+1)(3²+1)(3^4+1)(3^8+1)……(3^64+1)
原式＝0.5﹙3²－1﹚﹙3²＋1﹚﹙3^4＋1﹚﹙3^8＋1﹚……﹙3^64+1﹚
＝0.5﹙3^4－1﹚﹙3^4＋1﹚﹙3^8＋1﹚……﹙3^64+1﹚
＝0.5﹙3^8－1﹚﹙3^8＋1﹚……﹙3^64+1﹚
...

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(3+1)(3²+1)(3^4+1)(3^8+1)……(3^64+1)
原式＝0.5﹙3²－1﹚﹙3²＋1﹚﹙3^4＋1﹚﹙3^8＋1﹚……﹙3^64+1﹚
＝0.5﹙3^4－1﹚﹙3^4＋1﹚﹙3^8＋1﹚……﹙3^64+1﹚
＝0.5﹙3^8－1﹚﹙3^8＋1﹚……﹙3^64+1﹚
＝0.5﹙3^128－1﹚
＝﹙3^128／2﹚－0.5

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