[SOLVED] CS代写 CSI2101/UOttawa/MdH/W22

Use mathematical induction to prove that 1·1!+2·2!+…+n·n! = (n+1)!−1, whenever n is a positive integer.
Use mathematical induction to prove that 3n < n! if n is an integer greater than 6. Problem 3Use mathematical induction to prove that 6 divides n3 − n whenever n is a non- negative integer.Use mathematical induction to prove that 21 divides 4n+1 + 52n−1 whenever n is a positive integer.Copyright By PowCoder代写加微信 assignmentchef

Use strong induction to show that every positive integer can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 20 = 1, 21 = 2, 22 =4,andsoon.
1/2 CSI2101/UOttawa/MdH/W22

Let b be a fixed integer and j a fixed positive integer. Show that if P (b), P (b + 1), …, P(b+j) are true and [P(b)∧P(b+1)∧…∧P(k)] → P(k+1) is true for every integer k ≥ b + j, then P(n) is true for all integers n with n ≥ b.
Find the flaw with the following “proof” that an = 1 for all nonnegative integers n, whenever a is a nonzero real number.
Basis Step: a0 = 1 is true by the definition of a0.
Inductive Step: Assume that aj = 1 for all nonnegative integers j with j ≤ k. Then
ak+1=ak·ak =1·1=1.
Given that fn is the nth Fibonacci number. Show that fn+1fn−1 − fn2 = (−1)n when n is a positive integer.
2/2 CSI2101/UOttawa/MdH/W22

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