Question

Let A = (1 + 3 + 5 + +17+19) and B = (2 + 4 + 6 + + 18+ 20). What is the
value of |AB|?

Answer 1

To find the value of |AB|, compute the values of A and B using the sum formula. Take the absolute difference to find |AB| = 10.

Step-by-step explanation:

To find the value of |AB|, we need to first compute the values of A and B. A is the sum of odd numbers from 1 to 19, and B is the sum of even numbers from 2 to 20. The sum of odd numbers can be found using the formula S = n * (2a + (n-1)d) / 2, where n is the number of terms, a is the first term, and d is the common difference. In this case, n = 10, a = 1, and d = 2. Plugging these values into the formula, we get A = 10 * (2(1) + (10-1)(2)) / 2 = 100. Similarly, the sum of even numbers can be found using the same formula, but with a = 2. Plugging in the values, we get B = 10 * (2(2) + (10-1)(2)) / 2 = 110. Now, to find the value of |AB|, we simply take the absolute difference between A and B, which is |AB| = |100 - 110| = 10.

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