Recursion
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Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of non negative integers to the set of integers. If f is well
defined, find a formula for f(n) when n is a non negative integer and prove that your formula is valid.
a) f(0) = 1,f(n) = - f(n - 1) for n >= 1
b) f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n - 3) for n>=3
c) f(0) = 0, f(1) = 1, f(n) = 2f(n + 1) for n >= 2
d) f(0) = 0, f(1) = 1, f(n) = 2f(n - 1) for n >= 1
e) f(0) = 2, f(n) = fen - 1) if n is odd and n >= 1 and f(n) = 2f(n - 2) if n >= 2
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Solution Summary
Recursion is demonstrated for proposed functions.
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Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of non negative integers to the set of integers. If f is well
defined, find a formula for f(n) when n is a non negative integer and prove that your formula is valid.
a) f(0) = 1,f(n) = - f(n - 1) for n >= 1
b) f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n - 3) for n>=3
c) f(0) = 0, f(1) = 1, f(n) = 2f(n + 1) for n >= 2
d) f(0) = 0, ...
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