Question

化简计算

(1+1/2)(1+1/2的平方)(1+1/2的4次方)(1+1/2的8次方)(1+1/2的16次方)咋解

Answer 1

这个题目可以首先乘以(1-1/2)这个因子，最后再除以这个因子即可，如下：
(1+1/2)(1+1/2的平方)(1+1/2的4次方)(1+1/2的8次方)(1+1/2的16次方)
=(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)
=(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)
=(1-1/2^4)(1+1/2^4)(1+1/2^8)(1+1/2^16)/(1-1/2)
=(1-1/2^8)(1+1/2^8)(1+1/2^16)/(1-1/2)
=(1-1/2^16)(1+1/2^16)/(1-1/2)
=(1-1/2^32)/(1-1/2)
=2(1-1/2^32)
=2-1/2^31
这个是一种化简的思想，仅供参考，谢谢！