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1. Use mathematical induction to prove
Whenever n is a positive integer.
2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
INPUT: Integer n
OUTPUT: The sum of 1,...,n
S(n)
1. i ← 0
2. while n>0
3. do i ← i + n
4. n ← n-1
5. return(i)
Solve the following initial value problem y (3) - 5y'' - 22y' + 56 y= 0; y(0) = 1; y'(0) = -2; y''(0) = -4 Solution : r 3 - 5r 2 - 22r + 56 = (
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