Evaluate: sum_(n=0)^(2)(nx+3) Answer:

Evaluate n=0: Evaluate the expression for n=0. When n=0, the expression (nx+3) becomes (0*x+3), which simplifies to 3.Evaluate n=1: Evaluate the expression for n=1. When n=1, the expression (nx+3) becomes (1*x+3), which simplifies to x+3.Evaluate n=2: Evaluate the expression for n=2. When n=2, the expression (nx+3) becomes (2*x+3), which simplifies to 2x+3.Sum results n=0 to n=2: Sum the results from n=0 to n=2. Now we add the results from each step: 3 + (x+3) + (2x+3). This simplifies to 3 + x + 3 + 2x + 3.Combine like terms: Combine like terms. Adding the constants: 3 + 3 + 3 = 9. Adding the x terms: x + 2x = 3x. So the sum is 3x + 9.

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Evaluate: $\newline$ $\sum_{n=0}^{2}(n x+3)$ $\newline$ Answer:

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Algebra 2

Evaluate rational expressions II

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Q. Evaluate:

\newline

\sum_{n=0}^{2}(n x+3)

\newline

Answer:

Evaluate $n=0$ : Evaluate the expression for $n=0$ . $\newline$ When $n=0$ , the expression $(nx+3)$ becomes $(0\times x+3)$ , which simplifies to $3$ .
Evaluate $n=1$ : Evaluate the expression for $n=1$ . $\newline$ When $n=1$ , the expression $(nx+3)$ becomes $(1\times x+3)$ , which simplifies to $x+3$ .
Evaluate $n=2$ : Evaluate the expression for $n=2$ . $\newline$ When $n=2$ , the expression $(nx+3)$ becomes $(2\times x+3)$ , which simplifies to $2x+3$ .
Sum results $n=0$ to $n=2$ : Sum the results from $n=0$ to $n=2$ . Now we add the results from each step: $3 + (x+3) + (2x+3)$ . This simplifies to $3 + x + 3 + 2x + 3$ .
Combine like terms: Combine like terms. $\newline$ Adding the constants: $3 + 3 + 3 = 9$ . $\newline$ Adding the $x$ terms: $x + 2x = 3x$ . $\newline$ So the sum is $3x + 9$ .