a) The sum of the first n odd numbers, sum_odd(n), is defined as: sum_odd(n) = 1 + 3 + 5 + ... + 2n - 1, ne N i) Prove that sum_odd(n) is a recursive process. ii) As the result of i) above or otherwise, write a recursive C++ function: long int sum_odd(long n) { Il C++ code which computes the sum of the first n odd numbers.

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a) The sum of the first n odd numbers, sum_odd(n), is defined as:
sum_odd(n) = 1 + 3 + 5 + .. + 2n - 1, n eN
i) Prove that sum_odd(n) is a recursive process.
ii) As the result of i) above or otherwise, write a recursive C++ function:
long int sum_odd(long n)
{
II C++ code
}
which computes the sum of the first n odd numbers.
b) A certain function, h, has the recursive specification:
h(0) = 0
h(n+1) = odd(n) + h(n)
Where the odd function is defined as:
[1,if nis odd
odd(n) =
0,if nis even
Work out by hand, the recursive call:
h(5)
Transcribed Image Text:a) The sum of the first n odd numbers, sum_odd(n), is defined as: sum_odd(n) = 1 + 3 + 5 + .. + 2n - 1, n eN i) Prove that sum_odd(n) is a recursive process. ii) As the result of i) above or otherwise, write a recursive C++ function: long int sum_odd(long n) { II C++ code } which computes the sum of the first n odd numbers. b) A certain function, h, has the recursive specification: h(0) = 0 h(n+1) = odd(n) + h(n) Where the odd function is defined as: [1,if nis odd odd(n) = 0,if nis even Work out by hand, the recursive call: h(5)
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