MATH 115 Homework 2 (Summer 2008), Assignments of Number Theory

Download MATH 115 Homework 2 (Summer 2008) and more Assignments Number Theory in PDF only on Docsity! MATH 115: HOMEWORK 2 (SUMMER 2008) This homework is due on Tuesday, July 1st. (1) Let n ≥ 1 be an integer. (a) Prove the identity ( n k ) + ( n k + 1 ) = ( n + 1 k + 1 ) . [Hint: see page 39 of the book. Write it up in your own words.] (b) Prove the binomial theorem by induction on n. Book problems Do (write up and hand in!) the following exercises from the textbook: Pages 28–34: 7, 9, 10, 18 [Hint: use equation (1.7) from page 25], 19, 24, 26, 47 Pages 40–44: 1, 2, 3(a). Finally, take a look at the result of exercise 30 in page 31. Isn’t it neat? There is no need to hand this last problem in. 1