To simplify this expression, let's break it down into individual terms: (-1)^2 + (2^2) + (-3)^2 + (4^2) + (-5)^2 + ... + (n^2) The first term is (-1)^2 which equals 1. The second term is (2^2) which equals 4. The third term is (-3)^2 which equals 9. The fourth term is (4^2) which equals 16. In general, the nth term is (n^2). So, the simplified expression is: 1 + 4 + 9 + 16 + ... + (n^2) This is an arithmetic series with a common difference of 5, as each term is obtained by adding 5 to the previous term. To find the sum of an arithmetic series, you can use the formula: S = (n/2) * (first term + last term) In this case, the first term is 1 and the last term is n^2. So, the simplified expression becomes: S = (n/2) * (1 + n^2)

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