Answer:
The sum is 1575.
Explanation:
Consider the provided information.
It is given that positive integers smaller than 1000 and that can be written in the form

Where n is integer that means the value of n can be a positive number or a negative number.
For n = 0

For n=-1

For n=-2

For n = -3 the obtained number is not an integer.
Now consider the positive value of n.
For n=1

For n=2

For n=3

For n=4 the obtained number is greater than 1000.
Now add all the numbers.

Hence, the sum is 1575.