) Fill in the blanks to complete the proof of the following statement: "For all integers n > 1, 5n² + 3n is even." Proof: We proceed by induction on n. For each integer n > 1, let P(n) be the statement " (a). BASE CASE: When n = 1, we see that P(1) is true. (b) which is even. Therefore (c): Suppose that for some integer k > 1,. (e) = 22 for some z € Z. (d). That is INDUCTIVE STEP: We want to show that P(k+1) is true. That is, we want to show that (f) for some r € Z. By the induction hypothesis, we see that (g) (h) is an integer, we see that. (j). Thus, by the Principle of Mathematical Induction, P(n) is Since. (i) is even and true for all integers n 1.
) Fill in the blanks to complete the proof of the following statement: "For all integers n > 1, 5n² + 3n is even." Proof: We proceed by induction on n. For each integer n > 1, let P(n) be the statement " (a). BASE CASE: When n = 1, we see that P(1) is true. (b) which is even. Therefore (c): Suppose that for some integer k > 1,. (e) = 22 for some z € Z. (d). That is INDUCTIVE STEP: We want to show that P(k+1) is true. That is, we want to show that (f) for some r € Z. By the induction hypothesis, we see that (g) (h) is an integer, we see that. (j). Thus, by the Principle of Mathematical Induction, P(n) is Since. (i) is even and true for all integers n 1.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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Need to be done part c and d only
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