已知函数f(x)=ex-a(x+1)(a∈R)(e是自然对数的底数).
(1)若f(x)的图象与x轴相切,求实数a的值;
(2)当0≤a≤1时,求证:f(x)≥0;
(3)求证:对任意正整数n,都有(1+