(1+p)(1+p^2)(1+p^4).(1+p^(2^n))

问题描述:

(1+p)(1+p^2)(1+p^4).(1+p^(2^n))

(1)p=1时,原式=2×2×...×2=2ˆ(n+1);(2) p≠1时,(1+p)(1+p^2)(1+p^4).(1+p^(2^n))=(1-p)(1+p)(1+p^2)(1+p^4).(1+p^(2^n))/(1-p)=(1-p²)(1+p^2)(1+p^4).(1+p^(2^n))/(1-p)=.= {1-p^[2^(n+1)]...