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9. Let S₁, represent the given statement, and use mathematical induction to prove that Sn is true for every positive integer n. Sn: 1+5+9++ (4n − 3) = n(2n-1) Step 1: Show that S₁ is true when n = 1. a) Verify for S₂ for n = 1 Step 2: Show that Sk implies that Sk+1 b) Write the statement for n = k c) Write the statement for n = k + 1 d) Assume that Sk is true. Use algebra to show Sk implies Sk+1: Step 3: Conclusion e) Write a conclusion based upon (a)-(d)

9. Let S₁, represent the given statement, and use mathematical induction to prove that Sn is true for every positive integer n. Sn: 1+5+9++ (4n − 3) = n(2n-1) Step 1: Show that S₁ is true when n = 1. a) Verify for S₂ for n = 1 Step 2: Show that Sk implies that Sk+1 b) Write the statement for n = k c) Write the statement for n = k + 1 d) Assume that Sk is true. Use algebra to show Sk implies Sk+1: Step 3: Conclusion e) Write a conclusion based upon (a)-(d)

Advanced Engineering Mathematics
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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9. Let S₁, represent the given statement, and use mathematical induction to prove that Sn is true for every positive integer n. Sn: 1+5+9++ (4n − 3) = n(2n − 1) Step 1: Show that S₁ is true when n = 1. a) Verify for S₂ for n = 1 Step 2: Show that Sk implies that Sk+1 b) Write the statement for n = k c) Write the statement for n = k + 1 d) Assume that S is true. Use algebra to show Sk implies Sk+1: Step 3: Conclusion e) Write a conclusion based upon (a) - (d)
Transcribed Image Text:9. Let S₁, represent the given statement, and use mathematical induction to prove that Sn is true for every positive integer n. Sn: 1+5+9++ (4n − 3) = n(2n − 1) Step 1: Show that S₁ is true when n = 1. a) Verify for S₂ for n = 1 Step 2: Show that Sk implies that Sk+1 b) Write the statement for n = k c) Write the statement for n = k + 1 d) Assume that S is true. Use algebra to show Sk implies Sk+1: Step 3: Conclusion e) Write a conclusion based upon (a) - (d)
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