The factorial of a nonnegative integer n is written n! (pronounced \"n factorial

Question

The factorial of a nonnegative integer n is written n! (pronounced "n factorial")* and is defined as follows: n! = n middot (n - 1) middot (n- 2) middot...middot 1 (for values of n greater than 1) and n! = 1 (for n = 0 or n = 1). For example, 5! = 5 middot 4 middot 3 middot 2 middot 1, which is 120. Use while statements in each of the following: a) Write a program that reads a nonnegative integer and computes and prints its factorial. b) Write a program that estimates the value of the mathematical constant e by using the^formula: e = 1 + 1/1! + 1/2! + 1/3! + ... Prompt the user for the desired accuracy of e (i.e., the number of terms in the summation). c) Write a program that computes the value of ex by using the formula e^x = 1 + x/1! + x^2/2! + x^3/3! + ... Prompt the user for the desired accuracy of e (i.e., the number of terms in the summation).

Explanation / Answer

a) void main ()

{ int n,fact=1,i=1;

clrscr();

cout<<" enter the first number";

cin>>n;

//loop used to find factorial

while(i<=n)

{ fact=fact*i;

i++;

}

cout<<" the factorial of"<<n<<"is"<<fact;

getch();

}

int factorial(int);

b)

void main()
{
float sume=1;

int i=1,n;

cout<<“ Enter the limit: “;
cin>>n;

while(i<=n)
{

sume=sume+i/factorial(i);

i++;

}
cout<<“ e ="sume);
}

int factorial(int n)
{
int i,fact=1;
for(i=1;i<=n;i++)
fact=fact*i;
return fact;
}

c)

float factorial(int n)
    {
      float f=1;
      for(int i=1;i<=n;i++)
        f=f*i;
       return f;
    }

float series(int n,int x)
    {
      float h=1;
      for(int i=1;i<=n;i++)
       h=h*x;
      return h;
    }

int main()
    {
     clrscr();
     int n,x,i;
     float s=1;
     cout<<"Enter the value for 'n' & 'x': ";
     cin>>n>>x;
     for(i=1;i<=n;i++)
       s=s+series(i,x)/factorial(i);
     cout<<"e^x= "<<s;
     getch();
     return 0;
    }

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