![Chapo3760](/avatars/28501.jpg)
Chapo3760
12.03.2020 •
Mathematics
In order for a proof by mathematical induction to be valid, the basis statement must be true for the initial value of n and the argument of the inductive step must be correct for every integer greater than or equal to the initial value.
Consider the following statement.
For every integer n ≥ 1, 3n − 2 is even.
The following is a proposed proof by mathematical induction for the statement.
Since the property is true for n = 1, the basis step is true. Suppose the property is true for an integer k, where k ≥ 1.That is, suppose that 3k − 2 is even. We must show that
3k + 1 − 2 is even. Observe that 3k + 1 − 2 = 3k · 3 − 2 = 3k(1 + 2) − 2
= (3k − 2) + 3k · 2.
Now 3k − 2 is even by inductive hypothesis and 3k · 2 is even by inspection. Hence the sum of the two quantities is even (by Theorem 4.1.1). It follows that
3k + 1 − 2 is even, which is what we needed to show.
Identify the error(s) in the proof. (Select all that apply.)
3k + 1 − 2 ≠ (3k − 2) + 3k · 2
(3k − 2) + 3k · 2 ≠ 3k(1 + 2) − 2
3k − 2 is odd by the inductive hypothesis.
The inductive hypothesis is assumed to be true.
The basis step is false. It says that 31 − 2 is even.
Solved
Show answers
More tips
- H Health and Medicine How to Get Pregnant Faster?...
- S Style and Beauty Lamination of Hair: How it Works and What it is?...
- C Computers and Internet Best Applications for Your iPad: Review of the Best Candidates for Installation...
- S Style and Beauty Intimate Haircut: The Reasons, Popularity, and Risks...
- A Art and Culture When Will Eurovision 2011 Take Place?...
- S Style and Beauty How to Choose the Perfect Hair Straightener?...
- F Family and Home Why Having Pets at Home is Good for Your Health...
- H Health and Medicine How to perform artificial respiration?...
- H Health and Medicine 10 Tips for Avoiding Vitamin Deficiency...
- F Food and Cooking How to Properly Cook Buckwheat?...
Answers on questions: Mathematics
- M Mathematics True or false all whole numbers are integers why...
- M Mathematics Which of the following points satisfies the inequality...
- C Computers and Technology How to get to command prompt screen if i forgot password?...
- M Mathematics The challenger deep has previously been measured to have a depth of 10,994 meters. you have been sent to the part of the pacific ocean to verify this depth with an echo sounder. assuming...
- H History What was sir Francis Drake s last destination in his exploration route?...
- M Mathematics ANSWER IF YOU SEE ANWSER...
Ответ:
substitute
42=l x 6
7=l
Perimeter of a rectangle is 2l +2w
2(6)+ 2(7)
12+14=26ft is the perimeter
Hope this helps