for part 1 Part 1. Suppose we are using Proof by Induction to prove the formula
ID: 3732624 • Letter: F
Question
for part 1
Part 1. Suppose we are using Proof by Induction to prove the formula for the sum of the squares of the first n positive integers: n(n+1)(2n+1) -1 = Which of the following is the most appropriate base case for an inductive proof? Choose... Part 2. After showing that base case, we would make our inductive step. Which of the following is the most appropriate inductive hypothesis? k(k+1)(2k +1) a) Suppose that for all k >1, E 12 = - k(k+1)(2k + 1). b) Suppose that if E12 = 2, then Dk+1 = (k k+1 2 (k+1)(k+ 2)(2k + 3) (k+1)(k+ 2)(2k + 3) C) Suppose that for some k>1, it is the case that k2 = * k(k+1)(2k +1) d) Suppose that there is some k>1 such that E12 = Choose... Part 3. Based on the answers to Parts 1 and 2, what kind of induction is this? weak induction Check Finish attempt ...Explanation / Answer
part1: Show that this equality is true for n = 1
Base Case is to show that it is true for the least possible value. Since natural numbers start with 1, above is the answer
Part2:
d) Suppose that there is some k>1
Hypothesis is to to assume that it is true for some value
Part3:
Weak Induction
Because proving for n=k+1 depends on the hypothesis which is n=k. So, it is called weak induction.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.