(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)]} /(1-p)
(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)]} /(1-p)