Schwartz Moran
10/11/2023 · Elementary School
\( \left. \begin{array} { l } { k _ { 1 } = 2 ; k _ { 2 } = - 1 ; k _ { 3 } = 5 } \\ { \sum _ { i = 2 } ^ { 3 } ( k _ { i } - k _ { i } ^ { 2 } ) } \end{array} \right. \)
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Tutor-Verified Answer
Step-by-step Solution
To evaluate the expression \( \sum_{i=2}^{3} (k_i - k_i^2) \) using the given values of \( k_1, k_2, \) and \( k_3 \):
1. We first identify the values of \( k_2 \) and \( k_3 \):
- \( k_2 = -1 \)
- \( k_3 = 5 \)
2. Now we compute \( k_i - k_i^2 \) for \( i = 2 \) and \( i = 3 \):
- For \( i = 2 \):
\[
k_2 - k_2^2 = -1 - (-1)^2 = -1 - 1 = -2
\]
- For \( i = 3 \):
\[
k_3 - k_3^2 = 5 - 5^2 = 5 - 25 = -20
\]
3. Now we sum the results:
\[
\sum_{i=2}^{3} (k_i - k_i^2) = (k_2 - k_2^2) + (k_3 - k_3^2) = -2 + (-20) = -2 - 20 = -22
\]
Thus, the final result is:
\[
\sum_{i=2}^{3} (k_i - k_i^2) = -22
\]
Quick Answer
The result is -22.
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