论文部分内容阅读
习题是数学的心脏,数学课本习题是数学教材的重要组成部分。刻意探讨习题在解题中的应用,能帮助学生学会课本知识,又为指导学生提高解题能力开辟了一条有效的途径。高中代数(甲种本)第三册P.83,18(2)求证:C_(n-1)~m+C_(n-2)~m+…+C_(m-1)~m+C_m~m =C_n~(m+1) 这道习题的结论可来巧妙地解一些数列求和题。例1 求下列数列的和: (1)1+2+3+4+…+n; (2)1·2+2·3+3·4+…+n(n+1); (3)sum from k=1 to n k(k+1)(k+2)(k+3)…(k+p-1)。解:(1)1+2+3+4+…+n。
Exercises are the heart of mathematics and math textbook exercises are an important part of mathematics textbooks. The deliberate application of exercises in solving problems can help students learn textbook knowledge and open an effective way to guide students to improve their problem-solving abilities. High school algebra (A type) The third book P.83,18 (2) Proof: C_(n-1)~m+C_(n-2)~m+...+C_(m-1)~m+C_m~ m = C_n~(m+1) The conclusion of this exercise can be used to subtly solve some sequence summation problems. Example 1 Find the sum of the following columns: (1) 1+2+3+4+...+n; (2)1.2+2.3+3.4+...+n(n+1); (3) Sum from k=1 to nk(k+1)(k+2)(k+3)...(k+p-1). Solution: (1) 1+2+3+4+...+n.