MATHEMATICS

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MATHEMATICS

MATHEMATICS
Wenjian Liu (Instructor) MA-471 | Fall 2022 Homework 6Due Thursday, November 17 2022Problem 6.1 Prove that if nand kare integers with 1 k n, then k n k = n n 1 k 1 Problem 6.2 Prove the hockeystick identity r X k =0 n + k k = n + r+ 1 r Problem 6.3 Suppose that kand n kare xed positive integers. Justify the identity n X j = k j k = n + 1 k + 1 Problem 6.4 Suppose that nis a positive integer. Justify the identity n X k =0 n k 2 = 2n n 1

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