(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)麻烦用简便算法,

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 02:04:10

(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)麻烦用简便算法,
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
麻烦用简便算法,

(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)麻烦用简便算法,
(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)
=(3-1)(3+1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)/2
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)(3^32+1)/2
=……
＝(3^64-1)/2

(3-1)*...
(3^64-1)/2

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

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

原式乘以(3-1)再除以2
原式=(3^64-1)/2=1716841910146256242328924544640

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