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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)
Determine the solution to the following differential equation. x 2 y′′ + 3xy′ + 4 y = 0 Solution Find the roots to (3) first as generally. r(r -1) + 3r + 4 = 0 r
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This case will lead to similar problem that we've had all other time we've run in double roots or double eigenvalues. We only find a single solution and will require a second solut
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