Evaluate: sum_(n=2)^(5)(nx+4) Answer:

Understand summation notation: Understand the summation notation. The expression sum_(n=2)^(5)(nx+4) means we need to add the terms (nx+4) for each integer value of n starting from 2 and ending at 5.Calculate term for n=2: Calculate the term for n=2. Substitute n=2 into the expression (nx+4). (2x+4)Calculate term for n=3: Calculate the term for n=3. Substitute n=3 into the expression (nx+4). (3x+4)Calculate term for n=4: Calculate the term for n=4. Substitute n=4 into the expression (nx+4). (4x+4)Calculate term for n=5: Calculate the term for n=5. Substitute n=5 into the expression (nx+4). (5x+4)Add all terms together: Add all the terms together. Add the terms from Step 2 to Step 5. (2x+4) + (3x+4) + (4x+4) + (5x+4)Combine like terms: Combine like terms. Combine the x terms and the constant terms. 2x + 3x + 4x + 5x + 4 + 4 + 4 + 4 14x + 16

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Algebra 2

Evaluate rational expressions II

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Q. Evaluate:

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\sum_{n=2}^{5}(n x+4)

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Answer:

Understand summation notation: Understand the summation notation. $\newline$ The expression $\sum_{n=2}^{5}(nx+4)$ means we need to add the terms $(nx+4)$ for each integer value of $n$ starting from $2$ and ending at $5$ .
Calculate term for $n=2$ : Calculate the term for $n=2$ . $\newline$ Substitute $n=2$ into the expression $(nx+4)$ . $\newline$ $(2x+4)$
Calculate term for $n=3$ : Calculate the term for $n=3$ . $\newline$ Substitute $n=3$ into the expression $(nx+4)$ . $\newline$ $(3x+4)$
Calculate term for $n=4$ : Calculate the term for $n=4$ . $\newline$ Substitute $n=4$ into the expression $(nx+4)$ . $\newline$ $(4x+4)$
Calculate term for $n=5$ : Calculate the term for $n=5$ . $\newline$ Substitute $n=5$ into the expression $(nx+4)$ . $\newline$ $(5x+4)$
Add all terms together: Add all the terms together. $\newline$ Add the terms from Step $2$ to Step $5$ . $\newline$ $(2x+4) + (3x+4) + (4x+4) + (5x+4)$
Combine like terms: Combine like terms. $\newline$ Combine the $x$ terms and the constant terms. $\newline$ $2x + 3x + 4x + 5x + 4 + 4 + 4 + 4$ $\newline$ $14x + 16$