a) To compute: First 14 terms of the sequence of F N F N + 1 in decimal form (rounded to six decimal places when needed)

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Answer 1

Question

Chapter 13, Problem 55E

To determine

a)

To compute:

First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

To determine

b)

To explain:

The reason due to which FNFN+1→ϕ−1 while N gets larger.

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For each real-valued nonprincipal character x mod k, let A(n) = x(d) and F(x) = Σ : dn * Prove that F(x) = L(1,x) log x + O(1). n

By considering appropriate series expansions, e². e²²/2. e²³/3. .... = = 1 + x + x² + · ... when |x| < 1. By expanding each individual exponential term on the left-hand side the coefficient of x- 19 has the form and multiplying out, 1/19!1/19+r/s, where 19 does not divide s. Deduce that 18! 1 (mod 19).

Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.

Answer 2

Question

Chapter 13, Problem 55E

To determine

a)

To compute:

First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

To determine

b)

To explain:

The reason due to which FNFN+1→ϕ−1 while N gets larger.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 13, Problem 55E

To determine

a)

To compute:

First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

To determine

b)

To explain:

The reason due to which FNFN+1→ϕ−1 while N gets larger.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 13, Problem 55E

To determine

a)

To compute:

First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

To determine

b)

To explain:

The reason due to which FNFN+1→ϕ−1 while N gets larger.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 13, Problem 55E

To determine

a)

To compute:

First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

To determine

b)

To explain:

The reason due to which FNFN+1→ϕ−1 while N gets larger.

Answer 6

Chapter 13, Problem 55E

To determine

a)

To compute:

First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

Answer 7

Chapter 13, Problem 55E

To determine

a)

To compute:

First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

Answer 8

To determine

b)

To explain:

The reason due to which FNFN+1→ϕ−1 while N gets larger.

Answer 9

To determine

b)

To explain:

The reason due to which FNFN+1→ϕ−1 while N gets larger.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 13 - Compute the value of each of the following. a. F15...Ch. 13 - Compute the value of each of the following. a. F16...Ch. 13 - Prob. 3E Ch. 13 - Compute the value of each of the following. a....Ch. 13 - Describe in words what each of the expressions...Ch. 13 - Prob. 6E Ch. 13 - Given that F36=14,930,352 and F37=24,157,817, a....Ch. 13 - Prob. 8E Ch. 13 - Given that F36=14,930,352 and F37=24,157,817,...Ch. 13 - Given that F32=2,178,309 and F33=3,524,578, a.find...

a) To compute: First 14 terms of the sequence of F N F N + 1 in decimal form (rounded to six decimal places when needed)

Solution Summary: The author explains how to calculate the F_Nfn+1 term of Fibonacci series.

Concept explainers

Videos

a)

To compute:

First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

b)

To explain:

The reason due to which FNFN+1→ϕ−1 while N gets larger.

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Chapter 13 Solutions

a) To compute: First 14 terms of the sequence of F N F N + 1 in decimal form (rounded to six decimal places when needed)

Solution Summary: The author explains how to calculate the F_Nf­n+1 term of Fibonacci series.

Concept explainers

Videos

a) To compute: First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

b) To explain: The reason due to which FNFN+1→ϕ−1 while N gets larger.

Want to see the full answer?

Chapter 13 Solutions

Solution Summary: The author explains how to calculate the F_Nfn+1 term of Fibonacci series.

a)

To compute:

First 14 terms of the sequence of FNFN+1 in decimal form (rounded to six decimal places when needed)

b)

To explain:

The reason due to which FNFN+1→ϕ−1 while N gets larger.