The smallest possible value is −34, which is negative, not positive.
Let's explore different ways to parenthesize the expression
1−2−3−4−5−6−7−8 and find the smallest possible value.
If all the subtractions are performed from left to right without parentheses:
1−2−3−4−5−6−7−8=−34
To get the smallest positive value, we need to find a way to maximize the result of subtraction to make it as close to zero as possible. One approach could be to group the numbers in pairs, which results in a different calculation.
((((((((1−2)−3)−4)−5)−6)−7)−8)=−34
There's no way to parenthesize the expression differently in order to get a positive value. No matter how the parentheses are placed, the result will always be negative, specifically -34.
So, in this case, regardless of how you parenthesize the expression, the smallest possible value is −34, which is negative, not positive.
Question
what is the smallest positive value that the expression 1-2-3-4-5-6-7-8 can have when parenthesiezed in any way?