value = 1;
for(num1=1; num1<=i; num1++)
{
printf("%d", value);
value = value * (i - num1) / num1;
}
printf("\n");
Input: 5
Output:
1
11
121
1331
14641
The given code is a Pascal's Triangle number pattern generator. It prints the first 'i' rows of Pascal's Triangle, where 'i' is the input provided by the user. Each row of Pascal's Triangle consists of coefficients from the binomial expansion of (a + b)^n for a given 'n', starting with n = 0.
The code works as follows:
1. Initialize a variable `value` to 1.
2. Start a loop with a variable `num1` from 1 to 'i'.
3. Within the loop, print the current value of `value`.
4. Update `value` using the formula for the next value in Pascal's Triangle: `value = value * (i - num1) / num1`.
5. After the loop ends for each row, print a newline character to move to the next row.
The pattern printed corresponds to the coefficients of the binomial expansion of (a + b)^n for each row, where 'n' starts from 0 and goes up to 'i-1'.
In this example, the first row contains the coefficient of the binomial expansion for (a + b)^0, which is just 1. The second row contains the coefficients for (a + b)^1, which are 1 and 1. The third row corresponds to (a + b)^2, with coefficients 1, 2, and 1, and so on.
