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Evaluate the summation below. sum_(k=1)^(4)(-1-k^(2)) Answer:

Evaluate the summation below.\newline∑k=14(−1−k2) \sum_{k=1}^{4}\left(-1-k^{2}\right) \newlineAnswer:

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Full solution

Q. Evaluate the summation below.\newline∑k=14(−1−k2) \sum_{k=1}^{4}\left(-1-k^{2}\right) \newlineAnswer:
  1. Calculate k=2k=2: Now, let's calculate the term for k=2k=2:(−1−(2)2)=−1−4=−5\left(-1 - (2)^2\right) = -1 - 4 = -5
  2. Calculate k=3k=3: Next, calculate the term for k=3k=3:(−1−(3)2)=−1−9=−10\left(-1 - (3)^2\right) = -1 - 9 = -10
  3. Calculate k=4k=4: Finally, calculate the term for k=4k=4:(−1−(4)2)=−1−16=−17\left(-1 - (4)^2\right) = -1 - 16 = -17
  4. Sum all calculated terms: Now we sum all the terms we have calculated:\newlineSum = (−2)+(−5)+(−10)+(−17)(-2) + (-5) + (-10) + (-17)\newlineSum = −2−5−10−17-2 - 5 - 10 - 17\newlineSum = −34-34

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