Answer:
sum = (m+n)(n-m +1)/2
Explanation:
You want an expression for the sum of the numbers from m to n.
Totals
As the example shows, the sums of the numbers written forward and backward will be the sum of the numbers at the ends of the range:
m +n
Count
The number of times this sum is repeated is equal to the number of numbers in the range:
n -m +1
Sum of range
The sum of the numbers in the range will be half the product of these values:
sum = (m+n)(n-m +1)/2