Question

число 2019 разложили в сумму 10 различных натуральных чисел какое наименьшее значение может принимать разность между наибольшим и наименьшим из этих чисел​

Answer 1

Ответ:

10

Пошаговое объяснение:

Разность между наибольшим и наименьшим числом будет тогда, когда числа идут подряд.

197 + 198 + 199 + 200 + 201 + 202 + 203 + 204 + 205 + 206 = 2015 < 2019

198 + 199 + 200 + 201 + 202 + 203 + 204 + 205 + 206 + 207 = 2025 > 2019

Значит, нужно начать со 197, но к последним 4 числам прибавить 1:

197 + 198 + 199 + 200 + 201 + 202 + 204 + 205 + 206 + 207 = 2019

Разность между наибольшим и наименьшим:

207 - 197 = 10

Answer 2

Finding the Minimum Difference between the Largest and Smallest Numbers

To find the minimum difference between the largest and smallest numbers when the number 2019 is expressed as the sum of 10 different natural numbers, we can start by considering the possible values for the largest and smallest numbers in the sum.

Let's assume that the smallest number is x and the largest number is y. Since we want to minimize the difference between y and x, we can set up the following equation:

y - x = minimum difference

To find the minimum difference, we need to find the values of x and y that satisfy the equation and also meet the condition that the sum of the 10 numbers is equal to 2019.

Solving the Equation

To solve the equation, we can use the fact that the sum of an arithmetic series can be calculated using the formula:

Sum = (n/2)(first term + last term)

In this case, the sum is 2019 and the number of terms is 10. So we have:

2019 = (10/2)(x + y) 403.8 = x + y

Since we want to minimize the difference between y and x, we can try to make the difference as small as possible by making y as close to x as possible. One way to do this is to set y = x + 1.

Substituting y = x + 1 into the equation, we get:

403.8 = x + (x + 1) 403.8 = 2x + 1 402.8 = 2x x ≈ 201.4

Since x is a natural number, we can round it down to the nearest whole number:

x = 201

Substituting x = 201 into the equation y = x + 1, we get:

y = 201 + 1 y = 202

Therefore, the smallest value for the difference between the largest and smallest numbers is:

202 - 201 = 1

So the minimum difference between the largest and smallest numbers is 1.

Conclusion

When the number 2019 is expressed as the sum of 10 different natural numbers, the minimum difference between the largest and smallest numbers is 1.