) Fill in the blanks to complete the proof of the following statement: "For all integers n > 1, 5n? + 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) Since. (h) is an integer, we see that (j). Thus, by the Principle of Mathematical Induction, P(n) is (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, 5n? + 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) Since. (h) is an integer, we see that (j). Thus, by the Principle of Mathematical Induction, P(n) is (i) is even and true for all integers n 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve a and b part only
Transcribed Image Text:) Fill in the blanks to complete the proof of the following statement:
.....
“For all integers n > 1, 5n + 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 e 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)
Since.
and
(h) is an integer, we see that
(j). Thus, by the Principle of Mathematical Induction, P(n) is
(i) is even
true for all integers n > 1.
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