(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)等于多少?

来源：学生作业帮助网编辑：作业帮时间：2024/05/17 06:13:02

(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)等于多少?
(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)等于多少?

(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)等于多少?
思路：在原式乘上（2-1）,不断的产生平方差,可以巧解.
(2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)(2^64+1)
原式=(2-1)(2^1+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)
=(2^16-1)(2^16+1)(2^32+1)(2^64+1)
=(2^32-1)(2^32+1)(2^64+1)
=(2^64-1)(2^64+1)
=2^128-1

(2^1+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)
.
.
.
=(2^64-1)(2^64+1)
=2^128-1

乘以(2-1)
原式=2^128-1

1/2,1/4, (1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2009^2), (2+1)({2}^{2}+1)({2}^{4}+1)({2}^{8}+1).({2}^{64}+1)+1 巧算((2^1+1)(2^2+1)(2^4+1)(2^8+1)+1)/2^15 计算(2+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)+1 [(1+2^-(1/32)]*[(1+2^-(1/16)]*[(1+2^-(1/8)]*[(1+2^-(1/4)]*[(1+2^-(1/2)] (1-1/2^2)*(1-1/3^2)*(1-1/4^2)*.*(1-1/2002^2)*(1-1/2003^2) (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16), 1,2,4,4,1,( ) (2^1+1)(2^2+1)(2^4+1)(2^8+1)(2^16+1)(2^32+1)+1 (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^16 （1+1/2）（1+1/2^2）(1+1/2^4)(1+1/2^8)+1/2^15 计算题：（1+1/2) (1+1/2^2) (1+1/2^4) （1+1/2^8) +1/2^15 （1+1/2)(1+1/2^2)(1+1/2^4）（1+1/2^8)+1/2^15=? 1、1/2、1/4、1/7 计算:(2+1)(2^2+1)(2^4+1)(2^8+1)-2^16.计算：(2+1)(2^2+1)(2^4+1)(2^8+1)-2^16. 求和：sn=1/2^2-1+1/4^2-1+.1/(2n)^2-1 (2^2+1)*(2^4+1)*(2^8+1)*(2^16+1)*(2^32+1）