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sum_(n=0)^(2)(-n)=

n=02(n)= \sum_{n=0}^{2}(-n)=

Full solution

Q. n=02(n)= \sum_{n=0}^{2}(-n)=
  1. Arithmetic series calculation: The series is a finite arithmetic series where each term is the negative of the index nn. We will calculate each term and add them together.
  2. First term calculation: First term: when n=0n=0, the term is (0)(-0) which equals 00.
  3. Second term calculation: Second term: when n=1n=1, the term is (1)(-1) which equals 1-1.
  4. Third term calculation: Third term: when n=2n=2, the term is (2)(-2) which equals 2-2.
  5. Sum calculation: Now, we add all the terms together: 0+(1)+(2)0 + (-1) + (-2).
  6. Final result: The sum is 0120 - 1 - 2, which equals 3-3.

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