The Option D , Table Tools Insert
The information that a program requires in order to accomplish its objective is called input.
<h3>What is a program?</h3>
A program is a set of instructions by which the computer performs various tasks. The program is a sequence of instructions that are followed by the computer to run. An example is Microsoft Word.
A computer program comes under software. The sequence code of a program that is readable by humans is called source code. The program is run by information that is called input.
Thus, the data that a program needs in order to achieve its goal is referred to as input.
To learn more about the program, refer to the below link:
brainly.com/question/14368396
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Answer: reveal information about characters and their motivations
Explanation: to show data about the person to know if the person is mean or happy small or tall and more stuff and to say if they want to save the turtles or trees
Answer:
We have proven that the property of the Fibonacci sequence ![[F(n+1)]^2 =[F(n)]^2+F(n-1)F(n+2)](https://tex.z-dn.net/?f=%5BF%28n%2B1%29%5D%5E2%20%3D%5BF%28n%29%5D%5E2%2BF%28n-1%29F%28n%2B2%29)
holds by Mathematical Induction.
Explanation:
For n≥2. We prove that it holds for n=2, Assume that it holds for n=k and prove that it holds for n=k+1
F(1)=1
F(2) = 1
F(3) = F(3 − 1) + F(3 − 2)= F(2) + F(1)=1+1=2
F(4) = F(4 − 1) + F(4 − 2)= F(3) + F(2)=2+1=3
In
We prove it is true for n=2.
When n=2
![L.H.S: [F(n+1)]^2 = [F(2+1)]^2 = [F(3)]^2 = 2^2 =4\\R.H.S: [F(n)]^2+F(n-1)F(n+2) \\=[F(2)]^2+F(2-1)F(2+2)\\= [F(2)]^2+F(1)F(4)\\=1^2+1*3=1+3=4](https://tex.z-dn.net/?f=L.H.S%3A%20%5BF%28n%2B1%29%5D%5E2%20%3D%20%5BF%282%2B1%29%5D%5E2%20%3D%20%5BF%283%29%5D%5E2%20%3D%202%5E2%20%3D4%5C%5CR.H.S%3A%20%5BF%28n%29%5D%5E2%2BF%28n-1%29F%28n%2B2%29%20%20%5C%5C%3D%5BF%282%29%5D%5E2%2BF%282-1%29F%282%2B2%29%5C%5C%3D%20%5BF%282%29%5D%5E2%2BF%281%29F%284%29%5C%5C%3D1%5E2%2B1%2A3%3D1%2B3%3D4)
We assume it is true for n=k and prove that it holds for n=k+1.
When n=k+1 in
Substituting n=k+1 in the LHS: ![[F(n+1)]^2](https://tex.z-dn.net/?f=%5BF%28n%2B1%29%5D%5E2)
and applying: F(k+2)=F(k+1)+F(k)
![LHS: [F(k+2)]^2=[F(k+1)+F(k)]^2\\= [F(k+1)]^2+2F(k+1)F(k)+[F(k)]^2\\=[F(k+1)]^2+F(k)[2F(k+1)+F(k)]\\=[F(k+1)]^2+F(k)[F(k+1)+F(k+1)+F(k)]\\=[F(k+1)]^2+F(k)[F(k+1)+F(k+2)]\\=[F(k+1)]^2+F(k)F(k+3)](https://tex.z-dn.net/?f=LHS%3A%20%5BF%28k%2B2%29%5D%5E2%3D%5BF%28k%2B1%29%2BF%28k%29%5D%5E2%5C%5C%3D%20%5BF%28k%2B1%29%5D%5E2%2B2F%28k%2B1%29F%28k%29%2B%5BF%28k%29%5D%5E2%5C%5C%3D%5BF%28k%2B1%29%5D%5E2%2BF%28k%29%5B2F%28k%2B1%29%2BF%28k%29%5D%5C%5C%3D%5BF%28k%2B1%29%5D%5E2%2BF%28k%29%5BF%28k%2B1%29%2BF%28k%2B1%29%2BF%28k%29%5D%5C%5C%3D%5BF%28k%2B1%29%5D%5E2%2BF%28k%29%5BF%28k%2B1%29%2BF%28k%2B2%29%5D%5C%5C%3D%5BF%28k%2B1%29%5D%5E2%2BF%28k%29F%28k%2B3%29)
Substituting n=k+1 in the RHS :![[F(n)]^2+F(n-1)F(n+2)](https://tex.z-dn.net/?f=%5BF%28n%29%5D%5E2%2BF%28n-1%29F%28n%2B2%29)
RHS=![[F(K+1)]^2+F(K+1-1)F(K+1+2)=[F(k+1)]^2+F(k)F(k+3)](https://tex.z-dn.net/?f=%5BF%28K%2B1%29%5D%5E2%2BF%28K%2B1-1%29F%28K%2B1%2B2%29%3D%5BF%28k%2B1%29%5D%5E2%2BF%28k%29F%28k%2B3%29)
Since the LHS=RHS
Therefore, the property is true.
FOR REFERENCE
When n=k in
Substituting n=k in the LHS: and applying: F(k+1)=F(k)+F(k-1)
![LHS: [F(k+1)]^2=[F(k)+F(k-1)]^2\\= [F(k)]^2+2F(k)F(k-1)+[F(k-1)]^2\\=[F(k)]^2+F(k-1)[2F(k)+F(k-1)]\\=[F(k)]^2+F(k-1)[F(k)+F(k)+F(k-1)]\\=[F(k)]^2+F(k-1)[F(k)+F(k+1)]\\=[F(k)]^2+F(k-1)F(k+2)\\Substituting \: n=k \:in\: th\:e RHS :[F(n)]^2+F(n-1)F(n+2)](https://tex.z-dn.net/?f=LHS%3A%20%5BF%28k%2B1%29%5D%5E2%3D%5BF%28k%29%2BF%28k-1%29%5D%5E2%5C%5C%3D%20%5BF%28k%29%5D%5E2%2B2F%28k%29F%28k-1%29%2B%5BF%28k-1%29%5D%5E2%5C%5C%3D%5BF%28k%29%5D%5E2%2BF%28k-1%29%5B2F%28k%29%2BF%28k-1%29%5D%5C%5C%3D%5BF%28k%29%5D%5E2%2BF%28k-1%29%5BF%28k%29%2BF%28k%29%2BF%28k-1%29%5D%5C%5C%3D%5BF%28k%29%5D%5E2%2BF%28k-1%29%5BF%28k%29%2BF%28k%2B1%29%5D%5C%5C%3D%5BF%28k%29%5D%5E2%2BF%28k-1%29F%28k%2B2%29%5C%5CSubstituting%20%5C%3A%20n%3Dk%20%5C%3Ain%5C%3A%20th%5C%3Ae%20RHS%20%3A%5BF%28n%29%5D%5E2%2BF%28n-1%29F%28n%2B2%29)
![RHS=[F(K)]^2+F(K-1)F(K+2)](https://tex.z-dn.net/?f=RHS%3D%5BF%28K%29%5D%5E2%2BF%28K-1%29F%28K%2B2%29)
LHS=RHS
