Question: Exercise 3 (25 points) Proof by induction Let us prove this formula: = = ( ) = ( )(+ ) a) (4 points) Try this

Exercise 3 (25 points) Proof by induction Let us prove this formula: = = ( ) = ( )(+ ) 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). b) Let us prove this expression using induction a. (5 points) Show the base (basis) case b. Show the induction step by answering these questions: i. (4 points) What is your hypothesis to use for the induction step? ii. (12 points) Now, complete the induction step Exercise 3 (25 points) Proof by induction Let us prove this formula:

Exercise 3 (25 points) Proof by induction Let us prove this formula: n S= 2-1)^k (-1)^(n + 1) 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). b) Let us prove this expression using induction a. (5 points) Show the base (basis) case b. Show the induction step by answering these questions: i. (4 points) What is your hypothesis to use for the induction step? ii. (12 points) Now, complete the induction step

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