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.
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.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![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.
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[J[K] * B[k][);
CIJN = 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?
iii) The complete matrix C?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e0ee837-2e4c-4e67-a72a-fe55a823d8a4%2F8826ca1d-39af-43ba-b997-b11964d6faed%2F7qfo9sc_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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.
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[J[K] * B[k][);
CIJN = 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?
iii) The complete matrix C?
Expert Solution
Step 1
As per guidelines, Im supposed to answer the first question, so i request you repost the other question as separate question.
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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