9. Let S₁, represent the given statement, and use mathematical induction to prove that Sn is true for every positive integer n. Sn: 4+10+16++ (6n − 2) = n(3n + 1) Step 1: Show that S is true when n = 1. a) Verify for S, 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 S, implies Sk+1: Step 3: Conclusion e) Write a conclusion based upon (a) - (d)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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: 4 + 10 + 16 + ·+ (6n − 2) = n(3n + 1)
Step 1: Show that S is true when n = 1.
a) Verify for Sn 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 S, 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: 4 + 10 + 16 + ·+ (6n − 2) = n(3n + 1) Step 1: Show that S is true when n = 1. a) Verify for Sn 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 S, implies Sk+1: Step 3: Conclusion e) Write a conclusion based upon (a)-(d)
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