Question

The sum of the first n positive integers is 1/2 (n²+ n ) . Check the expression for the first 5 positive integers. Then use the expression to find the sum of the first 14 positive integers.

Answer 1

The sum of the first 5 positive integers is 15. The sum of the first 14 positive integers is 105.

Step-by-step explanation:

To check the expression for the first 5 positive integers, we can substitute n = 5 into the expression 1/2 (n²+ n). So, the sum would be 1/2 (5² + 5) = 1/2 (25 + 5) = 1/2 (30) = 15.

To find the sum of the first 14 positive integers using the expression, we substitute n = 14 into the expression 1/2 (n²+ n). So, the sum would be 1/2 (14² + 14) = 1/2 (196 + 14) = 1/2 (210) = 105.