The connections and representation of Pascal Triangles, Difference sequences and Matrices

파스칼의 삼각형, 계차수열 및 행렬의 연계와 표현

It is well-known in the literature that the general term of a sequence can be represented by a linear combination of binomial coefficients. The theorem and its known proofs are not easy for highschool students to understand. In this paper we prove the theorem by a pictorial method and by a very short and easy inductive method to make the problem easy and accessible enough for highschool students.