Using the pairing method 1+100, 2+99, ..., 50+51, which expression equals the total sum from 1 to 100?

Using the pairing method 1+100, 2+99, ..., 50+51, which expression equals the total sum from 1 to 100?

• A. 50 × 101
• B. 101 × 60
• C. 250 × 20
• D. 70 × 70

Answer: (A)

Pairing the numbers from 1 to 100 uses symmetry: the smallest and largest add to the same total. Pair 1 with 100, 2 with 99, and so on, up to 50 with 51. Each pair sums to 101, and there are 50 such pairs, so the total is 50 × 101, which equals 5050. This matches the familiar result for the sum of the first 100 integers. The other expressions would yield different values, so they don’t represent the total.

Pairing the numbers from 1 to 100 uses symmetry: the smallest and largest add to the same total. Pair 1 with 100, 2 with 99, and so on, up to 50 with 51. Each pair sums to 101, and there are 50 such pairs, so the total is 50 × 101, which equals 5050. This matches the familiar result for the sum of the first 100 integers. The other expressions would yield different values, so they don’t represent the total.