Still don’t know how to solve this?

When first encountering the problem of summing numbers from 1 to 200, many tend to think of adding each number individually, which is time-consuming and impractical. However, the pairing method provides a neat shortcut. This technique relies on recognizing patterns within the sequence. By pairing the first and last numbers (1 and 200), we observe their sum is 201. Next, pairing the second and the second-to-last numbers (2 and 199) also results in 201, and this pattern continues for all pairs. Since there are 200 numbers, pairing them in twos creates 100 pairs, each totaling 201. Multiplying 201 by 100 gives the sum of the entire sequence: 20,100. I've personally used this approach in teaching students who often find long addition tedious. This visualization not only simplifies calculations but also builds stronger number sense and pattern recognition skills. Mastering this method can help in solving a variety of arithmetic series problems quickly. Moreover, this approach can be generalized. For any consecutive numbers from 1 to n, where n is even, pairing the first and last numbers results in a constant sum, multiplied by the number of pairs (n divided by 2). For odd n, the median number is left unpaired but can be added after summing paired numbers. Using such strategies enhances problem-solving efficiency and deepens understanding of mathematical series, proving that math can be both logical and elegant.