For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
(15 + 14 + 13 + 12 + 11 + ...)
minus
(12 + 11 + 10 + ...)
30
To find the value of *16 - *13, we need to calculate the sum of the positive integers less than 16 and subtract the sum of the positive integers less than 13.
For *x, which represents the sum of positive integers less than x, we can use the formula to calculate it.
The formula to calculate the sum of positive integers less than a given number x is:
*n = (x - 1) * (x) / 2
Let's calculate *16:
*n = (16 - 1) * (16) / 2
*n = 15 * 16 / 2
*n = 240
So, *16 is equal to 240.
Now, let's calculate *13:
*n = (13 - 1) * (13) / 2
*n = 12 * 13 / 2
*n = 78
So, *13 is equal to 78.
Finally, we can calculate *16 - *13:
*16 - *13 = 240 - 78
*16 - *13 = 162
Therefore, the value of *16 - *13 is 162.