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4. (2 points) Evaluate3Qk=1(−1)k+1 sin ‹πk .A. 2 − √22B.√2 − 22C. 2 − √32D.√3 − 22E. cos ‰πk Ž

Question

  1. (2 points) Evaluate3Qk=1(−1)k+1 sin ‹πk .A. 2 − √22B.√2 − 22C. 2 − √32D.√3 − 22E. cos ‰πk Ž
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Solution

The question is asking to evaluate the sum of the series for k=1 to 3 of the expression (-1)^(k+1) * sin(πk).

Let's evaluate this step by step:

For k=1, the expression becomes (-1)^(1+1) * sin(π*1) = 1 * 0 = 0.

For k=2, the expression becomes (-1)^(2+1) * sin(π*2) = -1 * 0 = 0.

For k=3, the expression becomes (-1)^(3+1) * sin(π*3) = 1 * 0 = 0.

So, the sum of the series for k=1 to 3 is 0 + 0 + 0 = 0.

None of the provided options (A. 2 - √22, B. √2 - 22, C. 2 - √32, D. √3 - 22, E. cos πk) match this result. There might be a mistake in the question or the provided options.

This problem has been solved

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