a)Find closed-form formulas for B0(n), B1(n), and B2(n). (b) Find a closed-form formula for B3(n), and assuming that your formulas from part (a) are true, and prove the formula for B3(n) correct using induction. (c) Find an expression for A(4, 2) but with variables.
a)Find closed-form formulas for B0(n), B1(n), and B2(n). (b) Find a closed-form formula for B3(n), and assuming that your formulas from part (a) are true, and prove the formula for B3(n) correct using induction. (c) Find an expression for A(4, 2) but with variables.
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
Let A(m, n) be a function A: N× N → N , where N is the natural numbers. A(m, n) is defined by:
A(0, n) = n + 1 ∀n ≥ 0 (for all n >=0)
A(m, 0) = A(m-1, 1) ∀m > 0, (for all m>0)
A(m, n) = A(m-1, A(m, n-1)) ∀m,n > 0. (for all m and n>0)
Let B0, B1, B2, … be functions Bt: N→ N where Bt(n) = A(t, n).
a)Find closed-form formulas for B0(n), B1(n), and B2(n).
(b) Find a closed-form formula for B3(n), and assuming that your formulas from part (a) are true, and prove the formula for B3(n) correct using induction.
(c) Find an expression for A(4, 2) but with variables.
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