3. Create a C program to read a positive integer n and to verify the mathematical...
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3. Create a C program to read a positive integer n and to verify the mathematical expression: 1+3+5+ ... + (2n-1) = n² Need to prove that the equation is valid for n = 1 For n = 1, we obtain [2(1) - 1] = 1², so this holds for n = 1 Assume the equation is true for n, and prove the equation is true for n + 1 Assume: 1+3+5 + ... + (2n-1) = n² Prove: 1+3+5+...+ (2(n + 1) − 1) = (n + 1)² - Proof: 1+3+5+...+ (2(n + 1) - 1) =1+3+5+ ... + (2n-1) + (2n+2-1) = n² + (2n+2-1) (by assumption) = n² + 2n+1 = (n+1)² By induction, for every positive integer n, the expression is 1+3+5+ ... + (2n-1) = n². 3. Create a C program to read a positive integer n and to verify the mathematical expression: 1+3+5+ ... + (2n-1) = n² Need to prove that the equation is valid for n = 1 For n = 1, we obtain [2(1) - 1] = 1², so this holds for n = 1 Assume the equation is true for n, and prove the equation is true for n + 1 Assume: 1+3+5 + ... + (2n-1) = n² Prove: 1+3+5+...+ (2(n + 1) − 1) = (n + 1)² - Proof: 1+3+5+...+ (2(n + 1) - 1) =1+3+5+ ... + (2n-1) + (2n+2-1) = n² + (2n+2-1) (by assumption) = n² + 2n+1 = (n+1)² By induction, for every positive integer n, the expression is 1+3+5+ ... + (2n-1) = n².
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Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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