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How did they go from 30(2^k-1) to 15(2^k)? Please explain

How did they go from 30(2^k-1) to 15(2^k)? Please explain

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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How did they go from 30(2^k-1) to 15(2^k)? Please explain
Rest part Let K be any 'integen with Suppose that for every integen coith osisk fi =- 3. a+ a. This Sy the induction hy pothesis Noco by definition of fo , fi, fz, Apply the inductim hy pothesis to fix nd fkt. we have KH fixtt 7.(8.84+8.5*) m 1o (8.2*+ 2.5" 41. g* + 14.5k 20 sk-I 21.gK – 30 gk1 + 14.5K – 205* = 81.- 152K+ 14.5k - 4.5s 6 gK + 1u sk - 4.5k ニ 6. ak + 19 5k 3. a.2k + 2.5. 5k 3. a k+) + &.sk+)
Transcribed Image Text:Rest part Let K be any 'integen with Suppose that for every integen coith osisk fi =- 3. a+ a. This Sy the induction hy pothesis Noco by definition of fo , fi, fz, Apply the inductim hy pothesis to fix nd fkt. we have KH fixtt 7.(8.84+8.5*) m 1o (8.2*+ 2.5" 41. g* + 14.5k 20 sk-I 21.gK – 30 gk1 + 14.5K – 205* = 81.- 152K+ 14.5k - 4.5s 6 gK + 1u sk - 4.5k ニ 6. ak + 19 5k 3. a.2k + 2.5. 5k 3. a k+) + &.sk+)
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