Question: 3. Create a C program to read a positive integer n and to verify the mathematical expression: 1+3+5+ ... + (2n-1) = n Need
3. Create a C program to read a positive integer n and to verify the mathematical expression: 1+3+5+ ... + (2n-1) = n Need to prove that the equation is valid for n = 1 For n = 1, we obtain [2(1) - 1] = 1, 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) = n Prove: 1+3+5+...+ (2(n + 1) 1) = (n + 1) - Proof: 1+3+5+...+ (2(n + 1) - 1) =1+3+5+ ... + (2n-1) + (2n+2-1) = n + (2n+2-1) (by assumption) = n + 2n+1 = (n+1) By induction, for every positive integer n, the expression is 1+3+5+ ... + (2n-1) = n.
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