求(1+1)*(1+1/2)*(1+1/4)*(1+1/8)*.*(1+1/2048)

问题描述:

求(1+1)*(1+1/2)*(1+1/4)*(1+1/8)*.*(1+1/2048)

(1+1)*(1+1/2)*(1+1/4)*(1+1/8)*.*(1+1/2048)
=(1+1)*2*(1-1/2)*(1+1/2)*(1+1/4)*(1+1/8)*.*(1+1/2048)
=(1+1)*2*(1-1/4)*(1+1/4)*(1+1/8)*.*(1+1/2048)
=……
=(1+1)*2*(1-1/2048)*(1+1/2048)
=2*2*(1-1/2^12)
=4-(1/2^10)