计算:(2+1)(2的平方+1)(2的四次方+1).(2的32次方+1)的值.
问题描述:
计算:(2+1)(2的平方+1)(2的四次方+1).(2的32次方+1)的值.
答
(2+1)(2^2+1)(2^4+1)...(2^32+1)
=(2-1)(2+1)(2^2+1)(2^4+1)...(2^32+1)
=(2^2-1)(2^2+1)(2^4+1)...(2^32+1)
.
=(2^32-1)(2^32+1)
=2^64-1