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ove that f- 3. 2" + 2. 5" for each integer n 2 0. roof by strong mathematical induction: Let the property P(n) be the equation f-3. 2" + 2 5. "e will show that P(n) is true for every integer n 2 0. how that P(0) and P(1) are true: elect P(0) from the choices below. o P(0) - 3. 2° +2. 50 O-3-20 +2-50 O fo -5 O P(0) - -fo

ove that f- 3. 2" + 2. 5" for each integer n 2 0. roof by strong mathematical induction: Let the property P(n) be the equation f-3. 2" + 2 5. "e will show that P(n) is true for every integer n 2 0. how that P(0) and P(1) are true: elect P(0) from the choices below. o P(0) - 3. 2° +2. 50 O-3-20 +2-50 O fo -5 O P(0) - -fo

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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Suppose that fgr fr f2 is a sequence defined as follows. fo = 5, f, = 16, fk- 7f-1-10f-2 for every integer ka 2 Prove that f - 3. 2" + 2.5n for each integer na 0. Proof by strong mathematical induction: Let the property P(n) be the equation f- 3. 2 + 2- 5. We will show that P(n) is true for every integer n a 0. Show that P(0) and P(1) are true Select P(0) from the choices below. lo P(0) - 3. 20 + 2. 50 O-3- 20 + 2-50 O P(0) - fo Select P(1) from the choices below. O P(1) - f O4- 16 0-3-21+2-s O P(1) - 3-21 + 2 - P(0) and P(1) are true because 3- 20 + 2-s0 -5 and 3. 21 + 2.5- 16. Show that for every integer k 2 1, if P() is true for each integer i from 0 through k, then P(k+ 1) is trues We must show that f 3-2*+12-5*+1 This is the inductive hypothesis v Let k be any integer with k 2 1, and suppose that for every integer i with osisk,- Now, by definition of fo fa f2- - -10f-1 Apply the inductive hypothesis to and f-1 and complete the proof as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen
Transcribed Image Text:Suppose that fgr fr f2 is a sequence defined as follows. fo = 5, f, = 16, fk- 7f-1-10f-2 for every integer ka 2 Prove that f - 3. 2" + 2.5n for each integer na 0. Proof by strong mathematical induction: Let the property P(n) be the equation f- 3. 2 + 2- 5. We will show that P(n) is true for every integer n a 0. Show that P(0) and P(1) are true Select P(0) from the choices below. lo P(0) - 3. 20 + 2. 50 O-3- 20 + 2-50 O P(0) - fo Select P(1) from the choices below. O P(1) - f O4- 16 0-3-21+2-s O P(1) - 3-21 + 2 - P(0) and P(1) are true because 3- 20 + 2-s0 -5 and 3. 21 + 2.5- 16. Show that for every integer k 2 1, if P() is true for each integer i from 0 through k, then P(k+ 1) is trues We must show that f 3-2*+12-5*+1 This is the inductive hypothesis v Let k be any integer with k 2 1, and suppose that for every integer i with osisk,- Now, by definition of fo fa f2- - -10f-1 Apply the inductive hypothesis to and f-1 and complete the proof as a free response. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen
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