Reference no: EM131927290
The Lucas numbers are defined recursively by the formulas
L1 = 1, L3 = 3, and for all n ≥ 3, Ln = Ln-1 + Ln-2.
The first few Lucas numbers are
1, 3, 4, 7, 11, 18...
This definition is similar to that of the Fibonacci numbers Fn, except that F1 = and F2 = 1
Using induction, prove that for all integers, n > 1,
Ln = Fn-1 + Fn+1.
You may need to recall that the Fibonacci numbers are the sequence, {Fn}, that is defined via the formula:
F1 = 1, F2 = 1, and for all n ≥ 3, Fn = Fn-1 + Fn-2.
Hint. When you work on this, you'll likely find that you need to know not only information about the k-th Lucas number, but also the (k-1)-th Lucas number. Don't forget to correctly identify what is your conditional statement, P(k)! You should adjust your induction steps accordingly:
new base cases: you need to show that both P(2) and P(3) are true.
new inductive hypothesis: given k ∈ N generic and k ≥ 3, assume that P(k-1) and P(k) are both true.
new inductive step: prove that P(k+1) is true.
|
Briefly discuss what is meant by just cause
: Briefly discuss what is meant by just cause. Briefly expand on the definition of employment-at-will, and discuss the exceptions to this doctrine.
|
|
How many cubic yards of concrete are? needed
: A new sidewalk will be 6 feet wide, 300 feet? long, and filled to a depth of 3 inches ?(0.25 ?foot) with concrete. How many cubic yards of concrete are? needed?
|
|
Two investments together yield at least
: If I invest a total of $12000 in two accounts. $8000 in a saving account paying 6% annual simple interest, at what rate does the remainder of the money
|
|
Create an environment in which employee issues are identify
: Include recommendations on a strategy that Elora Jean & Co. can incorporate to proactively avoid grievances. Your recommendation should include a way to create.
|
|
Fibonacci numbers fn
: This definition is similar to that of the Fibonacci numbers Fn, except that F1 = and F2 = 1
|
|
Compile an annotated bibliography
: Select Health care section - You are required to compile an Annotated bibliography of 5 peer-reviewed journal articles - briefly outline the topics
|
|
Discuss about the selected behavior
: Each of us perceives "ethics" from our own point of reference as to what is or is not ethical. This assignment asks you to consider ethics and whistleblowers.
|
|
Estimate the population of fur seal pups in the rookery
: In late? August, 900 fur seal pups were captured. Of? these, 223 had been tagged. Based on these? figures, estimate the population of fur seal pups.
|
|
Review problem on hostage crises
: In a hostage crises, is it ethical for a government to agree to grant a terrorist immunity if he releases the hostages, even though the government has every.
|