Discrete mathematics Given that a, = 0, a, = 0, a2 = 1 andan =3an-1 - 3an-2 + an-3 for all integers n > 3, prove thatAn =nED for all non-negative integers n using strong induction.2

Name: Discrete mathematics Given that a, = 0, a, = 0, a2 = 1 andan =3an-1 -
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Description: Discrete mathematics Given that a, = 0, a, = 0, a2 = 1 andan =3an-1 - 3an-2 + an-3 for all integers n > 3, prove thatAn =nED for all non-negative integers n using strong induction.2

Take n =0 a0=00-12=0 hence it is true for n= 0 take n= 1 a1=11-12=0 So it is also true for n=1 check…

Answered: Given that a, = 0, a, = 0, a2 = 1 and…

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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Discrete mathematics

Given that a, = 0, a, = 0, a2 = 1 and
an =
3an-1 - 3an-2 + an-3 for all integers n > 3, prove that
An =
nED for all non-negative integers n using strong induction.
2

Expert Solution

Step 1

Take n =0

$a_{0} = \frac{0 (0 - 1)}{2} = 0$ hence it is true for n= 0

take n= 1

$a_{1} = \frac{1 (1 - 1)}{2} = 0$

So it is also true for n=1

check for n=2

$a_{2} = \frac{2 (2 - 1)}{2} = 1$

So it is also true for n=2

check for n=3

$a_{3} = \frac{3 (3 - 1)}{2} = 3$

Now check for a₃ by using the given relation

$a_{3} = 3 a_{2} - 3 a_{1} + a_{0} = 3 (1) - 3 (0) + 0 = 3$

So it is also true for n =3

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