Sum of 500 consecutive integers is 250 . what is the product same 500 numbers

You can see that since the sum is less than the number of terms and also since the sum is positive, it should start from negative numbers and go on to positive numbers. Which means one of the term should be 0. And hence The product must be equal to 0.

To put it more formally,

x+x+1+x+2⋯+x+499=250

So our eq is:

x+x+1+x+2⋯+x+499=250

500x+1+2+⋯+499=250

500x+500×4992=250

500(x+4992)=250

500(2x+4992)=250

250(2x+499)=250

2x+499=1

2x=−498

x=−249

So starting from −249 it'll go on upto 250

(As

|{−249⋯0}|=250

|{1⋯250}|=250 )

Since 0 is also an element of this set.

The product will be −249×−248⋯×0×⋯250=0

Step-by-step explanation:

Hope it is helpful...

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step-by-step explanation: