Provided a function that would be defined fo every natural number n as

mattgondek4

mattgondek4

Answered question

2021-09-03

Provided a function that would be defined fo every natural number n as: g(n)=22+14+18++12n1+12n COnjecture a closed form form for g(n) (a simple expression devoid of signs or dots) while also using mathematical induction to prove that the conjecture is true.

Answer & Explanation

irwchh

irwchh

Skilled2021-09-04Added 102 answers

Prove the following using the principle of mathematical induction: j=1nj=12n1+12n,for n>0 Hint: Determine the base case value. Since the base case value must be greater than 0, the base case value will be set to the next integer after 0: The base case value is n = 1 Hint: Find a proposition P(n) to be proved for all n>0. For each integer n, let P(n) be the statement j=1nj=21n+2n. Consider the following properties: base case: P(1) is true inductive step: For all integers k>0, if P(k) is true, then P(k + 1) is true If the above properties hold, then for each n element Z where n>0, the statement P(n) is true Hint: Substitute n = 1 into the claim to verify P(1). Substitute n = 1 into j=1nj=21n+2n: j=11j=211+21 Hint: Simplify both sides. Simplify both sides to check for validity: Answer: 132, therefore the base case is false and the proof is unsuccessful

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