(1+2分之1)(1+2的平方分之1)(1+2的立方分之1)(1+2的4方分之1).(1+2的16次方分之1)

问题描述:

(1+2分之1)(1+2的平方分之1)(1+2的立方分之1)(1+2的4方分之1).(1+2的16次方分之1)

应该是这样吧:
(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)
=2(1-1/2) (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)(1+1/2^16)
=(1-1/2^2)(1+1/2^2)(1+1/2^3)(1+1/2^4)(1+1/2^8)(1+1/2^16)
=2(1-1/2^4)(1+1/2^4)(1+1/2^8)(1+1/2^16)
=2(1-1/2^8)(1+1/2^8)(1+1/2^16)
=2(1-1/2^16)(1+1/2^16)
=2(1+1/2^32)
=2-1/2^31