Hw-7: C++ OOP to print a fibonacci series.

 

Fibonacci Series in C++

Fibonacci Series in C++: In case of fibonacci series, next number is the sum of previous two numbers for example 0, 1, 1, 2, 3, 5, 8, 13, 21 etc. The first two numbers of fibonacci series are 0 and 1.

Do the following two ways:

• Fibonacci Series without recursion
• Fibonacci Series using recursion

Hw-6: Write a c++ OOP to find factorial using loop in C++

In this program, we will learn how to find factorial of a given number using C++ program? Here, we will implement this program with and without using user define function.

Logic:

1. Input a number
2. Initialize the factorial variable with 1
3. Initialize the loop counter with N (Run loop from number (N) to 1)
4. Multiply the loop counter's value with factorial variable

Program to find factorial using loop in C++

Enter an integer number: 6
Factorial of 6 is = 720    

What is factorial?

Answer: 

Factorial !

Example: 4! is shorthand for 4 × 3 × 2 × 1

The factorial function (symbol: !) says to multiply all whole numbers from our chosen number down to 1. Examples: 4! = 4 × 3 × 2 × 1 = 24 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040 1! = 1

We usually say (for example) 4! as "4 factorial", but some people say "4 shriek" or "4 bang"

Calculating From the Previous Value

We can easily calculate a factorial from the previous one:

As a table:

n	n!
1	1	1	1
2	2 × 1	= 2 × 1!	= 2
3	3 × 2 × 1	= 3 × 2!	= 6
4	4 × 3 × 2 × 1	= 4 × 3!	= 24
5	5 × 4 × 3 × 2 × 1	= 5 × 4!	= 120
6	etc	etc

• To work out 6!, multiply 120 by 6 to get 720
• To work out 7!, multiply 720 by 7 to get 5040
• And so on

Example: 9! equals 362,880. Try to calculate 10!

10! = 10 × 9!

10! = 10 × 362,880 = 3,628,800

So the rule is:

n! = n × (n−1)!

Which says

"the factorial of any number is that number times the factorial of (that number minus 1)"

So 10! = 10 × 9!, ... and 125! = 125 × 124!, etc.

What About "0!"

Zero Factorial is interesting ... it is generally agreed that 0! = 1.

It may seem funny that multiplying no numbers together results in 1, but let's follow the pattern backwards from, say, 4! like this:

And in many equations using 0! = 1 just makes sense.

Example: how many ways can we arrange letters (without repeating)?

• For 1 letter "a" there is only 1 way: a
• For 2 letters "ab" there are 1×2=2 ways: ab, ba
• For 3 letters "abc" there are 1×2×3=6 ways: abc acb cab bac bca cba
• For 4 letters "abcd" there are 1×2×3×4=24 ways: (try it yourself!)
• etc

The formula is simply n!

Now ... how many ways can we arrange no letters? Just one way, an empty space:

So 0! =
1