Evaluate the summation below. sum_(k=2)^(5)(-4k+2k^(2)) Answer:

Set up the problem: Understand the summation expression and set up the problem. We need to evaluate the sum of the expression (-4k + 2k^2) for each integer value of k from 2 to 5.Calculate for k=2: Calculate the sum for k=2. Substitute k=2 into the expression (-4k + 2k^2) to get the first term of the summation. First term = -4(2) + 2(2)^2 = -8 + 8 = 0.Calculate for k=3: Calculate the sum for k=3. Substitute k=3 into the expression (-4k + 2k^2) to get the second term of the summation. Second term = -4(3) + 2(3)^2 = -12 + 18 = 6.Calculate for k=4: Calculate the sum for k=4. Substitute k=4 into the expression (-4k + 2k^2) to get the third term of the summation. Third term = -4(4) + 2(4)^2 = -16 + 32 = 16.Calculate for k=5: Calculate the sum for k=5. Substitute k=5 into the expression (-4k + 2k^2) to get the fourth term of the summation. Fourth term = -4(5) + 2(5)^2 = -20 + 50 = 30.Find total sum: Add all the terms together to find the total sum. Total sum = First term + Second term + Third term + Fourth term = 0 + 6 + 16 + 30 = 52.

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Evaluate the summation below.

sum_(k=2)^(5)(-4k+2k^(2))
Answer:

Evaluate the summation below. $\newline$ $\sum_{k=2}^{5}\left(-4 k+2 k^{2}\right)$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the chain rule

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Q. Evaluate the summation below.

\newline

\sum_{k=2}^{5}\left(-4 k+2 k^{2}\right)

\newline

Answer:

Set up the problem: Understand the summation expression and set up the problem. $\newline$ We need to evaluate the sum of the expression $(-4k + 2k^2)$ for each integer value of $k$ from $2$ to $5$ .
Calculate for $k=2$ : Calculate the sum for $k=2$ . $\newline$ Substitute $k=2$ into the expression $(-4k + 2k^2)$ to get the first term of the summation. $\newline$ First term = $-4(2) + 2(2)^2 = -8 + 8 = 0$ .
Calculate for $k=3$ : Calculate the sum for $k=3$ . $\newline$ Substitute $k=3$ into the expression $(-4k + 2k^2)$ to get the second term of the summation. $\newline$ Second term = $-4(3) + 2(3)^2 = -12 + 18 = 6$ .
Calculate for $k=4$ : Calculate the sum for $k=4$ . $\newline$ Substitute $k=4$ into the expression $(-4k + 2k^2)$ to get the third term of the summation. $\newline$ Third term = $-4(4) + 2(4)^2 = -16 + 32 = 16$ .
Calculate for $k=5$ : Calculate the sum for $k=5$ . Substitute $k=5$ into the expression $(-4k + 2k^2)$ to get the fourth term of the summation. Fourth term = $-4(5) + 2(5)^2 = -20 + 50 = 30$ .
Find total sum: Add all the terms together to find the total sum. $\newline$ Total sum = First term + Second term + Third term + Fourth term = $0 + 6 + 16 + 30 = 52$ .