Question 1: a) i) Give an inductive formula for the sum of the first n odd numbers: 1 + 3 + 5 + ... + 2n -1 Show your induction process. ii) Use the proof by mathematical induction to prove the correctness of your inductive formula in i) above. .............................................................
Question 1:
a) i) Give an inductive formula for the sum of the first n odd numbers:
1 + 3 + 5 + ... + 2n -1
Show your induction process.
ii) Use the proof by mathematical induction to prove the correctness of your
inductive formula in i) above.
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b) The following C++ program segment computes C = A * B, where A is an “m” by “n”
matrix, B is an “n” by “r” matrix and C is an “m” by “r” matrix.
for (long int i = 0; i < m; i++)
for (long int j = 0; j < r; j++)
{
long double Sum = 0;
for (long int k = 0; k < n; k++)
Sum = Sum + A[i][k] * B[k][j];
C[i][j] = Sum;
}
How many times does the code iterate in computing
i) Sum?
ii) The j column of C, i.e. C[i][j] for a fixed i and j = 1, 2, ,3, ..., r?
th
iii) The complete matrix C?
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