That depends, what are the values of these numbers first?

Algebra Level 3

The sum of 2017 consecutive integers is 0. Is the product of these 2017 consecutive integers also 0?

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2 solutions

Freddie Hand
Jan 8, 2017

The consecutive integers cannot all be positive or negative, or the sum would be positive or negative, and 0 is neither. Therefore, there must be some positive integers and some negative integers, so the number 0 must be one of the integers, so the product of the integers is 0.

For this example we can consider the following numbers in the addition: -1008+-1007+...+1007+1008 and the result is 0. Then if the multiply all the previous numbers in one moment we have to multiply by 0 and the result of the multiplication is also 0.

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