san wrote:
x+y=200
all possible sums of the integers x and y pair?
If mentioned that x and y are positive.
For positive integers
x=1 y=199 sum =200
x=2 y=198 sum =200
..
..
..
x=200 y=0 sum =200
Sum of all positive integers is = \(200 \times 200\)
If x and y are not mentioned to be positive then the sum is infinite. because we can rewirte the pairs
x= -Infinity y = 200 + Infinity sum=200
..
..
x=-2 y=202 sum =200
x=-1 y=201 sum =200
x=0 y=200 sum =200
x=1 y=199 sum =200
x=2 y=198 sum =200
..
..
..
x=200 y=0 sum =200
Sum of all integers is = \(Infinity \times 200\)