Evaluate: sum_(n=3)^(6)(nx-3) Answer:

Understand summation notation: Understand the summation notation. The expression sum_(n=3)^(6)(nx-3) means we need to evaluate (nx-3) for each integer value of n from 3 to 6 and then sum the results.Evaluate for n=3: Evaluate the expression for n=3. Substitute n=3 into the expression (nx-3) to get (3x-3).Evaluate for n=4: Evaluate the expression for n=4. Substitute n=4 into the expression (nx-3) to get (4x-3).Evaluate for n=5: Evaluate the expression for n=5. Substitute n=5 into the expression (nx-3) to get (5x-3).Evaluate for n=6: Evaluate the expression for n=6. Substitute n=6 into the expression (nx-3) to get (6x-3).Sum the results: Sum the results from steps 2 to 5. Add the expressions obtained for each value of n: (3x-3) + (4x-3) + (5x-3) + (6x-3).Combine like terms: Combine like terms. Combine the x terms: 3x + 4x + 5x + 6x = 18x. Combine the constant terms: -3 - 3 - 3 - 3 = -12. So, the sum is 18x - 12.

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Algebra 2

Evaluate rational expressions II

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Q. Evaluate:

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\sum_{n=3}^{6}(n x-3)

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Answer:

Understand summation notation: Understand the summation notation. The expression $\sum_{n=3}^{6}(nx-3)$ means we need to evaluate $(nx-3)$ for each integer value of $n$ from $3$ to $6$ and then sum the results.
Evaluate for $n=3$ : Evaluate the expression for $n=3$ . Substitute $n=3$ into the expression $(nx-3)$ to get $(3x-3)$ .
Evaluate for $n=4$ : Evaluate the expression for $n=4$ . $\newline$ Substitute $n=4$ into the expression $(nx-3)$ to get $(4x-3)$ .
Evaluate for $n=5$ : Evaluate the expression for $n=5$ . Substitute $n=5$ into the expression $(nx-3)$ to get $(5x-3)$ .
Evaluate for $n=6$ : Evaluate the expression for $n=6$ . Substitute $n=6$ into the expression $(nx-3)$ to get $(6x-3)$ .
Sum the results: Sum the results from steps $2$ to $5$ . Add the expressions obtained for each value of $n$ : $(3x-3) + (4x-3) + (5x-3) + (6x-3)$ .
Combine like terms: Combine like terms. $\newline$ Combine the $x$ terms: $3x + 4x + 5x + 6x = 18x$ . $\newline$ Combine the constant terms: $-3 - 3 - 3 - 3 = -12$ . $\newline$ So, the sum is $18x - 12$ .