Concept explainers
a.
To Find:
a.
Answer to Problem 37E
False
Explanation of Solution
Given information:
Proof:
For
We get
As 121 is not a prime number
b.
To Find:
b.
Answer to Problem 37E
True.
Explanation of Solution
Given information:
Use Mathematical induction to prove the above-mentioned formula.
Concept used:
1.By using Mathematical induction technique we need to prove that this formula holds True for all the natural numbers. The first step is to prove True for
2.Second step by using induction hypothesis of mathematical induction we assume for
3.Third step is we need to prove that above formula is True for
Proof:
Put
We get
It True for
Let us assume it is True for
So
We need to prove it is True for
We need to prove equation-(2)
From equation-(1)
We get
Adding with
We get
We know
So
Which is equation-(2)
So
Which is True for
And hence the proof by Mathematical induction.
c.
To Find:
c.
Answer to Problem 37E
True
Explanation of Solution
Given information:
Use Mathematical induction to prove the above-mentioned formula.
Concept used:
1.By using Mathematical induction technique we need to prove that this formula holds True for all the natural numbers. The first step is to prove True for
2.Second step by using induction hypothesis of mathematical induction we assume for
3.Third step is we need to prove that above formula is True for
Proof:
Given formula is
Put
We get
It True for
Let us assume it is True for
So
We need to prove it is True for
As
So,
Which is True for
And hence the proof by Mathematical induction.
d.
To Find:
d.
Answer to Problem 37E
False
Explanation of Solution
Given information:
Proof:
Given formula is
Put
We get
Which is False
So,
e.
To Find:
e.
Answer to Problem 37E
True
Explanation of Solution
Given information:
Use Mathematical induction to prove the above-mentioned formula.
Concept used:
1.By using Mathematical induction technique we need to prove that this formula holds True for all the natural numbers. The first step is to prove True for
2.Second step by using induction hypothesis of mathematical induction we assume for
3.Third step is we need to prove that above formula is True for
Proof:
Given formula is
Put
We get
As 6 is divisible by 3
It True for
Let us assume it is True for
So
We need to prove it is True for
As
So,
Which is True for
And hence the proof by Mathematical induction.
f.
To Find:
f.
Answer to Problem 37E
True
Explanation of Solution
Given information:
Use Mathematical induction to prove the above-mentioned formula.
Concept used:
1.By using Mathematical induction technique we need to prove that this formula holds True for all the natural numbers. The first step is to prove True for
2.Second step by using induction hypothesis of mathematical induction we assume for
3.Third step is we need to prove that above formula is True for
Proof:
Given formula is
Put
We get
As 6 is divisible by 6
It True for
Let us assume it is True for
So
We need to prove it is True for
As
So
So,
Which is True for
And hence the proof by Mathematical induction.
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning