Look for a pattern in the expressions shown below. Use the pattern to write an expression for the sum of the whole numbers from 1 to n. Then find the sum of the whole numbers from 1 to 50.

1+2= 2•3/2 1+2+3= 3•4/2 1+2+3+4= 4•5/2

1+...+n = n(n+1)/2

To find the pattern in the expressions and write an expression for the sum of the whole numbers from 1 to n, let's analyze the given examples:

1 + 2 = 2 * 3/2
1 + 2 + 3 = 3 * 4/2
1 + 2 + 3 + 4 = 4 * 5/2

If we break down the equation, we can see that the left side represents the sum of numbers from 1 to a specific number (n), and the right side has a pattern involving the number n.

On the left side, the sum of the numbers is represented by adding them consecutively.

On the right side, the pattern shows that the value of n is multiplied by the next consecutive number (n + 1), and then divided by 2.

Hence, we can write the expression for the sum of the whole numbers from 1 to n as:

sum = n * (n + 1) / 2

To find the sum of the whole numbers from 1 to 50, substitute 50 in place of n:

sum = 50 * (50 + 1) / 2
sum = 50 * 51 / 2
sum = 2550 / 2
sum = 1275

Therefore, the sum of the whole numbers from 1 to 50 is 1275.