Determine all amounts of postage that can be formed using only 4-cent and 11-cent stamps. Prove your answer using strong induction. Be sure to show the base cases, the inductive hypothesis, and the inductive step.

Q: Use the principle of mathematical induction to prove the statement below. You should have an…

A: Given that a0=6, an=3an-1     for n≥1.To show: an=6.3n   for all integers n≥0.

Q: se for all integers nz2, tity = to shaw that for all integer

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Q: Let n be the number points scored by a team in a football game. What are the possible values of n,…

A: It is given that n be the number points scored by a team in a football game. It is asked to find…

Q: 1.50 Prove: 2+4+6++ 2n n(n+1) 1.51 Prove: 1+4+7+.+ 3n – 2 = n(3n-1) 1.52 Prove: 12 +22+32 + ... +n²…

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Q: 3. Suppose that a store offers gift certificates in denominations of 25 dollars and 40 dollars.…

A: We need to determine which amounts can be made from 25 dollars and 40 dollars. Since 25 and 40 are…

Q: n (7) Vn € N, Σi!i = (n + 1)! — 1. i=1

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Q: n(nº +5) is divisible by 6, for each integer n 0.

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Q: Use permutations to solve. From a cooler with 6 different kinds of soda, 4 are selected for 4…

A: nPr = n!/(n-r)!

Q: 2k > 1+ k

A: We have to prove 2k ≥ 1 + k for every natural number k

Q: use the mathematical induction to prove : 2" < n! < 3" , Vn E N* ,n 2 4

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Q: You are a pickle fanatic and only order your pickles online from Papa Pete’s Pickle Emporium. All…

A: The pickles are available only in sets of either three or seven jars. To prove: Any number of n…

Q: Consider the following recurrence relation: -{+ C(n) = if n = 0 n+ 3. C(n-1) if n > 0. Prove by…

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Q: Suppose Sn is the following sum. 1 1 Sn 1·2 ' n(n + 1) 2·3

A: To will find the explicit formula by using some algebraic calculations and then we prove that…

Q: 3. Let n e N. Prove by mathematical induction that > 3* = 4". k k=0

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Q: The local post office offers stamps worth 4 cents and 5 cents. Prove that we can make any postage…

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Q: marhs ASSIGHENT use mathematical Induction to thad prave (on-)(an+2) for bnt4 10 40 88 att nEN

A: To prove the given statement by mathematical induction.

Q: 5n + 3" > 22n+1 for all n E Z+

A: Here given as 5n+3n≥22n+1 for all n∈Z+ Put n=1 Then 5+3≥22+18≥8 It is true for n=1

Q: A shop gives gift cards in nominal 25 and 40k. determine the possible total amount that can be…

A: Proof at first, the amounts seem semi-random:

Q: Use mathematical induction to prove: For each natural number n, 6 divides (n3-n). I need to write a…

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Q: Clarissa is tearing her test (1 sheet of paper) into small pieces. She picks up a piece of paper and…

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Q: 1. For nENº, 12" – 5ª is divisible by 7 (Note: N° =NU{0}). %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: prove the statement is true by using Mathematical Induction.

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Q: Use the mathematical induction

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Q: Is this function:  a) both even and odd b) even c) neither even and odd d) odd

A: Simply if f(x)=f(-x) then function is even Now is f(x)+f(-x)=0 then its an odd function

Q: Use mathematical induction to prove the following equation is true for every positive integer of n.…

A: According to the given information it is required to prove

Q: If {an}=1 is defined as a₁ = 1, a₂ = 4, and an = -an-1 + 2an-2 +6n - 7 for n ≥ 3, then Vn € Z+, an =…

A: If the sequence ann=1∞ is defined as a1=1, a2=4, and an=-an-1+2an-2+6n-7 for n≥3, then ∀n∈ℤ+, an=n2.…

Q: Prove that for any positive integer n, there is a k e Z>o and ao, a1, . .. , ak E {0,1} such that k…

A: Please check later steps for detailed answer

Q: Clarissa is tearing her test (1 sheet of paper) into small pieces. She picks up a piece of paper and…

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Q: Prove by Mathematical Induction, for all integers n 2 3, that the sum of the interior angles of ar…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.