Proving Inf{a^n: n in Z+}=0 for 0<a<1 using the hint (1+h)^n >= 1 +nh

[Unassuming]

Given "a" with 0<a<1, prove that inf{a^n : n in Z+}=0

[HINT] Let h=(1-a)/a , show (1+h)^n >= 1 +nh


I have proven the second part of the hint using induction but I cannot figure out why this shows the statement holds.

I have gotten that the hint is the same as,

a^-n >= 1+nh , I don't know what I am not seeing.

Again, thank you in advance.

 

[Dick]

1+nh goes to infinity as n->infinity. That means a^(-n) goes to infinity. a^(n)=1/a^(-n). So?