Analysis, prove a period by induction

Question

Given that $F(x) = F(x+T)$ is $T$-periodic, prove by induction that $F(x) = F(x+nT)$ for all $n \in \mathbb N$.

Would appreciate some help with this... one of my finals practice questions.

Thanks.

Answer 1

Hint: Convince yourself that what's going on here is just this:

$$F(x+nT)=F(x+(n-1)T+T)=F(x+(n-1)T)=\cdots=F(x)$$

Now try and translate this into the formal framework of induction:

What are your induction start, hypothesis and step, respectively?