Evaluate the summation below. 7sum_(k=0)^(4)(4k-2k^(2)) Answer:

Evaluate Series: We need to evaluate the summation of the series given by the expression 7 times the sum from k equals 0 to 4 of (4k - 2k^2). We will do this by calculating the sum term by term and then multiplying by 7.Calculate Terms: First, let's calculate the sum without the factor of 7. We will substitute k = 0, 1, 2, 3, and 4 into the expression (4k - 2k^2) and find the sum of these values.Calculate Sum: For k = 0: (4*0 - 2*0^2) = 0. For k = 1: (4*1 - 2*1^2) = 4 - 2 = 2. For k = 2: (4*2 - 2*2^2) = 8 - 8 = 0. For k = 3: (4*3 - 2*3^2) = 12 - 18 = -6. For k = 4: (4*4 - 2*4^2) = 16 - 32 = -16. Now, we add these values together to get the sum.Multiply by 7: The sum is 0 + 2 + 0 - 6 - 16 = -20.Now, we multiply this sum by 7 to get the final answer. 7 * (-20) = -140.

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Evaluate the summation below.

7sum_(k=0)^(4)(4k-2k^(2))
Answer:

Evaluate the summation below. $\newline$ $7 \sum_{k=0}^{4}\left(4 k-2 k^{2}\right)$ $\newline$ Answer:

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Algebra 2

Sum of finite series starts from 1

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Q. Evaluate the summation below.

\newline

7 \sum_{k=0}^{4}\left(4 k-2 k^{2}\right)

\newline

Answer:

Evaluate Series: We need to evaluate the summation of the series given by the expression $7$ times the sum from $k = 0$ to $4$ of $(4k - 2k^2)$ . We will do this by calculating the sum term by term and then multiplying by $7$ .
Calculate Terms: First, let's calculate the sum without the factor of $7$ . We will substitute $k = 0, 1, 2, 3,$ and $4$ into the expression $(4k - 2k^2)$ and find the sum of these values.
Calculate Sum: For $k = 0$ : $(4\times0 - 2\times0^2) = 0$ . For $k = 1$ : $(4\times1 - 2\times1^2) = 4 - 2 = 2$ . For $k = 2$ : $(4\times2 - 2\times2^2) = 8 - 8 = 0$ . For $k = 3$ : $(4\times3 - 2\times3^2) = 12 - 18 = -6$ . For $k = 4$ : $(4\times4 - 2\times4^2) = 16 - 32 = -16$ . Now, we add these values together to get the sum.
Multiply by $7$ : The sum is $0 + 2 + 0 - 6 - 16 = -20$ .
Multiply by $7$ : The sum is $0 + 2 + 0 - 6 - 16 = -20$ .Now, we multiply this sum by $7$ to get the final answer. $\newline$ $7 \times (-20) = -140$ .