Question

Даны два целых числа А и В (А<В). Найти сумму всех целых чисел от А до В включительноВходные данные: ввести два целых числа А,В (1<=A, B<=100).Выходнфе данные: вывести сумму всех целых чисел от А до В включительно.Можно, пожалуйста, с объяснением.

Answer 1

var

  sum, a, b, i : integer;

begin

  read (a, b);

  sum := 0;

  for i := a to b do //Бежим по всем числам от а до б

    sum := sum + i; //и прибавляем каждое число к сумме

  writeln (sum);

end.

Answer 2

Finding the Sum of Integers from A to B

To find the sum of all integers from A to B inclusive, where A is less than B, you can use a simple mathematical formula. The sum of integers from 1 to N can be calculated using the formula:

Sum = (N * (N + 1)) / 2

Where N is the largest number in the range. In this case, we can use the formula to find the sum of integers from A to B.

Calculating the Sum

Let's calculate the sum of all integers from A to B inclusive using the provided values of A and B.

Given: - A = 3 - B = 7

We can calculate the sum using the formula: Sum = (B * (B + 1)) / 2 - ((A - 1) * A) / 2

Substituting the values of A and B: Sum = (7 * (7 + 1)) / 2 - ((3 - 1) * 3) / 2

Solving: Sum = (7 * 8) / 2 - (2 * 3) / 2 Sum = 56 / 2 - 6 / 2 Sum = 28 - 3 Sum = 25

So, the sum of all integers from 3 to 7 inclusive is 25.

Explanation

The formula for the sum of integers from 1 to N is derived from the arithmetic series formula. It's based on the fact that the sum of the first N natural numbers is equal to N * (N + 1) / 2. By subtracting the sum of integers from 1 to (A-1) from the sum of integers from 1 to B, we can find the sum of integers from A to B.

In this case, we used the formula to calculate the sum of integers from A to B, which resulted in the sum of 25 for the given values of A and B.