I have the following question as homework, and I am still clueless as to how to approach these problems. Just when I think I have a hand of how to solve card related problems, I get thrown another that just leaves me clueless. Any who, I would appreciate any help afforded in explaining the problem below
How many strictly increasing sequences of integers are there that begin with $1$ and end with $n$, where $n>1$? For example, if $n =4$, there are $4$ such sequences: $1,4;\quad 1,2,4;\quad 1,3,4;\quad 1,2,3,4$ . Prove your answer with strong induction