C program to print pascal's triangle up to 30 rows

Here is a simple C program to print Pascal's triangle.




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#include<conio.h>
long double fact(int);
void main()
{
  long a[30][50];
  int n,i,j,k;
  clrscr();
  printf("Enter the number of rows ");
  scanf("%d",&n);
  for(i=0;i<n;i++)
  {
    for(k=2*n+2;k>2*i;k--)
      printf(" ");
    for(j=0;j<=i;j++)
    {
      a[i][j]=(long)(fact(i)/(fact(i-j)*fact(j)));
      printf(" %2ld ",a[i][j]);
    }
    printf("\n\n");
  }
  getch();
}
long double fact(int n)
{
  if(n<=1)
    return 1;
  else
    return fact(n-1)*n;
}

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First of all what is pascals triangle ,From the the binomial theorem we have

(a+b)ⁿ =ⁿC₀aⁿb⁰+  ⁿC₁a^n-1b¹+……………+  ⁿC_ra^n-rb^r  +………….+ ⁿC_na⁰bⁿ

where ⁿC_r =n!/(r!*(n-r)!)

thus (a+b)²=a² +2ab+ b²

in similar way (a+b)³=a³ +3a² b+3ab² +b³

from the above equations we get following pattern

                            1

1                  1

               1           2           1

       1           3              3         1

This is called Pascal’s triangle .Now to print Pascal triangle we have fact(i)/(fact(i-j)*fact(j) this is same as the formula we discuss  above .I have used recursion to calculate factorial .Notice that I have taken the return type of fact functions long double because through int we can print up to 8 rows only and using long double we can print up to 30 rows ,also I have type cast the result  and stored in array and than simply print it .               

Any questions regarding to program please write in comments.