Suppose we have a set like (1,2,3) then there is only one way to choose 3 consecutive number...its (1,2,3)....for a sets of 4 (1,2,3,4) we have 3 ways ( (1,2,3), (2,3,4), (1,2,3,4)) for five its 8 ,for 6 its 20, for 7 its 47 and so on....So for a given N, I can get the answer by applying brute force, and calculating all such subset having 3 or more consecutive number. Here I am just trying to find out a pattern, a technique to get the number of all such subset for a given N. The problem is further generalized to .....discover m consecutive number within a set of size N.
marked as duplicate by Marc van Leeuwen, William, tomasz, Ｊ. Ｍ., Norbert Oct 3 '12 at 20:08
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.