I was working on a probability exercise and then I get a little bit confused. The question was probability of getting a straight flush in 52 cards deck, so I was wondering how many scales there are for each suit. I came up with this table $$\begin{array}{c| c c c c c } 1 & A& 2 & 3 & 4 & 5 \\ 2 & 2& 3 & 4& 5& 6 \\ \vdots & \vdots & & & & \vdots \\ 10 & 10& J& Q& K& A \end{array} $$ So total number of scales in a suit is $10$. Could this results be generalized so
Given $n$ natural numbers (we choose to not consider $0)$ how many consecutive line of $m$ elemets there are ($m\leq n $)?
This table reasoning could also apply so $$\begin{array}{c| c c c c c } 1 & 1& 2 & 3 & \cdots & m \\ \vdots & \vdots & & & & \vdots \\ n-m+1 & n-m+1& n-m+2& n-m+3& \cdots& n \end{array} $$ So we can conclude that the number we are searching is $n-m+1$? Is this a valid proof, there are other methods to prove this? Sorry if the question look silly, thanks for any help!