MATH 221 Midterm: MATH 221 Drexel Sample Exam Solutions

• School: Drexel University
• Department: Mathematics
• Course: MATH 221
• Professor: All

Document Summary

We apply the induction method for the proof: base step: for n = 1, the left-hand side is 1 2 = 2, and the right-hand side is 1(1+1)(1+2) = 2, so the statement is true: inductive step: suppose the statement is true for n = k, i. e. , +(k+1)(k+2) k(k + 1)(k + 2) + 3(k + 1)(k + 2) 3 (k + 1)(k + 2)(k + 3) 3 i. e. , the statement is true for n = k + 1: the conclusion: the statement is true for all natural n. Let p (n) be the statement that a postage of n cents can be formed using just 3-cent and 5-cent stamps. Solution. (a) 8 = 3 + 5, 9 = 3 + 3 + 3, 10 = 5 + 5, so that p (8), Since k 2 8, by the induction hypothesis we have that p (k 2) is true, i. e. , a postage of.