Identify series and terms: Identify the series and its terms. The series is given by sum_(k=1)^(2)(3-k), which means we need to find the sum of the terms (3-k) for each integer value of k from 1 to 2.Calculate first term: Calculate the first term of the series. When k=1, the first term is (3-1) which equals 2.Calculate second term: Calculate the second term of the series. When k=2, the second term is (3-2) which equals 1.Find sum of terms: Find the sum of the terms. The sum of the series is the sum of the first and second terms: 2 + 1.Perform final addition: Perform the addition to find the final sum. 2 + 1 equals 3.

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Grade 8

Powers with negative bases

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\sum_{k=1}^{2}(3-k)=

Identify series and terms: Identify the series and its terms. $\newline$ The series is given by $\sum_{k=1}^{2}(3-k)$ , which means we need to find the sum of the terms $(3-k)$ for each integer value of $k$ from $1$ to $2$ .
Calculate first term: Calculate the first term of the series. $\newline$ When $k=1$ , the first term is $(3-1)$ which equals $2$ .
Calculate second term: Calculate the second term of the series. $\newline$ When $k=2$ , the second term is $(3-2)$ which equals $1$ .
Find sum of terms: Find the sum of the terms. $\newline$ The sum of the series is the sum of the first and second terms: $2 + 1$ .
Perform final addition: Perform the addition to find the final sum. $2 + 1$ equals $3$ .