计算:(1+2)(1+2^2)(1+2^4)(1+2^8)(1+2^16)(1+2^32)(1+2^64)

问题描述:

计算:(1+2)(1+2^2)(1+2^4)(1+2^8)(1+2^16)(1+2^32)(1+2^64)


原式
=(2-1)(2+1)(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)
=(2^4-1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=(2^8-1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
=……
=2^128-1

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