Let $(x_{n_{k}})$ be a subsequence of $(x_n)$. Prove rigorously by induction that the indices of the subsequence satisfy $n_{k}\geq k$.
Im not sure how to start this problem (other than the obvious starting with a base case then doing the inductive step). Im not sure what exactly the question is asking. Please help.
By definition of a subsequence $n_1 <n_2<...$. Use a simple induction argument to show that $n_k \geq k$ for all $k$.