1-(1-p)^n>p^n (0

1-(1-p)^n>p^n (0
1-(1-p)^n>p^n (0

1-(1-p)^n>p^n (0
证明：设f(n)=p^n+(1-p)^n,因为0＜p＜1,所以0＜1-p＜1,所以函数f(x)=p^x+(1-p)^x在(0,+∞）上是减函数,于是f(n)≤f(1)=p+1-p=1,即p^n+(1-p)^n≤1,即1-(1-p)^n≥p^n.