Need Help with B) b,

Exercise 3 (25 points) Proof by induction Let us prove this formula: n S=(-1)*k2 = (-1)"n(n+1) { (n) 2 k=0 a) (4 points) Try this expression with n = 3. Evaluate S using the two expressions (the sum and the closed form fraction and check whether they yield the same result). S = %=0(1)*k2= (1902 + (-1)-12 + (-1)322 + (-1)332 = -6 in k= = = -6 S = (-1)"n(n+1) (-1)33(3+1) 2 2 b) Let us prove this expression using induction a. (5 points) Show the base (basis) case: (-1)"n(n+1) S(O): S= 2 2 b. Show the induction step by answering these questions: . (4 points) What is your hypothesis to use for the induction step? If S(O) ii. (12 points) Now, complete the induction step (-1)0(0+1) = 0 =