6.60. Below is given a proof of a result. Which result is being proved and which proof technique is being used? Proof First observe that a = 8 = 3-1+5 and az = 11 = 3 - 2+5. Thus, an = 3n +5 for n = 1 and n = 2. Assume that a = 3i + 5 for all integers i with 1 2. Since k+1>3, it follows that 5ar – 4ak-1 – 9 = 5 (3k + 5) – 4 (3k +2) – 9 = 15k + 25 – 12k – 8 – 9 = 3k + 8 = 3 (k+1) +5. ak+1

6.60. Below is given a proof of a result. Which result is being proved and which proof technique is being used? Proof First observe that a = 8 = 3-1+5 and az = 11 = 3 - 2+5. Thus, an = 3n +5 for n = 1 and n = 2. Assume that a = 3i + 5 for all integers i with 1 2. Since k+1>3, it follows that 5ar – 4ak-1 – 9 = 5 (3k + 5) – 4 (3k +2) – 9 = 15k + 25 – 12k – 8 – 9 = 3k + 8 = 3 (k+1) +5. ak+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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Question

Using complete sentences and terms such as Suppose, consider, then, so, thus if necessary.

6.60. Below is given a proof of a result. Which result is being proved and which proof technique is being used?
Proof First observe that a = 8 = 3-1+5 and az = 11 = 3 - 2+5. Thus, an = 3n +5 for n = 1 and n = 2. Assume that a = 3i + 5 for all
integers i with 1<i<k, where k > 2. Since k+1>3, it follows that
5ar – 4ak-1 – 9 = 5 (3k + 5) – 4 (3k +2) – 9
= 15k + 25 – 12k – 8 – 9 = 3k + 8 = 3 (k+1) +5.
ak+1

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