数学 简便方法,要有过程.
〔(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)〕/2^64
简便方法,要有过程.
参考答案:〔(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)〕/2^64
=[(2-1)(2+1)(2^2+1)(2^4+1)...(2^64+1)]/2^64
=[(2^2-1)(2^2+1)...(2^64+1)]/2^64
=.....
=[(2^64-1)(2^64+1)]/2^64
=[2^128-1]/2^64
=2^64-2^(-64)