Understanding the series: Understand the series and its terms. We need to calculate the sum of the series where each term is given by the expression (2k+2) and k ranges from 0 to 2.Calculating the first term: Calculate the first term of the series. Substitute k=0 into the expression (2k+2) to find the first term. First term: (2*0+2) = 2Calculating the second term: Calculate the second term of the series. Substitute k=1 into the expression (2k+2) to find the second term. Second term: (2*1+2) = 4Calculating the third term: Calculate the third term of the series. Substitute k=2 into the expression (2k+2) to find the third term. Third term: (2*2+2) = 6Summing all the terms: Sum all the terms of the series. Add the first, second, and third terms together to get the total sum. Total sum: 2 + 4 + 6 = 12

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Algebra 2

Composition of linear and quadratic functions: find a value

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\sum_{k=0}^{2}(2 k+2)=

Understanding the series: Understand the series and its terms. $\newline$ We need to calculate the sum of the series where each term is given by the expression $(2k+2)$ and $k$ ranges from $0$ to $2$ .
Calculating the first term: Calculate the first term of the series. $\newline$ Substitute $k=0$ into the expression $(2k+2)$ to find the first term. $\newline$ First term: $(2\times 0+2) = 2$
Calculating the second term: Calculate the second term of the series. $\newline$ Substitute $k=1$ into the expression $(2k+2)$ to find the second term. $\newline$ Second term: $(2\times 1+2) = 4$
Calculating the third term: Calculate the third term of the series. $\newline$ Substitute $k=2$ into the expression $(2k+2)$ to find the third term. $\newline$ Third term: $(2\times 2+2) = 6$
Summing all the terms: Sum all the terms of the series. $\newline$ Add the first, second, and third terms together to get the total sum. $\newline$ Total sum: $2 + 4 + 6 = 12$