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What is the main objective of the proof of sum of squares by induction?
What is the main objective of the proof of sum of squares by induction?
- To prove the sum of squares is always an even number
- To show that the sum of squares is equal to ninjas
- To prove the formula for the sum of squares using mathematical induction (correct)
- To prove the sum of squares is always finite
What is the claim in the proof of sum of cubes by induction?
What is the claim in the proof of sum of cubes by induction?
- k=1 k3 = n · (n + 1) 2 (correct)
- k=1 k5 = n · (n + 1) 2
- k=1 k4 = n · (n + 1) 2
- k=1 k2 = n · (n + 1) 2
What is the purpose of the base step in a proof by induction?
What is the purpose of the base step in a proof by induction?
- To prove the statement is true for only one value of n (correct)
- To prove the statement is true for all negative integers
- To prove the statement is true for all positive integers
- To prove the statement is true for all real numbers
What is the purpose of the inductive step in a proof by induction?
What is the purpose of the inductive step in a proof by induction?
What is the formula for the sum of squares proved in the given text?
What is the formula for the sum of squares proved in the given text?
What is the assumption made in the inductive step of the proof of sum of cubes by induction?
What is the assumption made in the inductive step of the proof of sum of cubes by induction?
What is the goal of the inductive step in the proof of sum of cubes by induction?
What is the goal of the inductive step in the proof of sum of cubes by induction?
What is the role of mathematical induction in the proof of sum of squares and sum of cubes?
What is the role of mathematical induction in the proof of sum of squares and sum of cubes?
What is the format of the proof of sum of squares and sum of cubes by induction?
What is the format of the proof of sum of squares and sum of cubes by induction?
What is the main difference between the proof of sum of squares and sum of cubes by induction?
What is the main difference between the proof of sum of squares and sum of cubes by induction?
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