Evaluate: sum_(n=1)^(3)(nx+1) Answer:

Understand the problem: Understand the problem. We need to evaluate the sum of the expression (nx + 1) for n ranging from 1 to 3. This means we will substitute n with 1, 2, and 3 into the expression and sum the results.Substitute n = 1: Substitute n = 1 into the expression and evaluate. For n = 1, the expression becomes (1x + 1). Calculate the expression for n = 1: 1x + 1 = x + 1.Substitute n = 2: Substitute n = 2 into the expression and evaluate. For n = 2, the expression becomes (2x + 1). Calculate the expression for n = 2: 2x + 1 = 2x + 1.Substitute n = 3: Substitute n = 3 into the expression and evaluate. For n = 3, the expression becomes (3x + 1). Calculate the expression for n = 3: 3x + 1 = 3x + 1.Sum the results: Sum the results from steps 2, 3, and 4. Add the expressions from each step: (x + 1) + (2x + 1) + (3x + 1). Combine like terms: x + 2x + 3x + 1 + 1 + 1 = 6x + 3.

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Algebra 2

Simplify variable expressions using properties

Full solution

Q. Evaluate:

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\sum_{n=1}^{3}(n x+1)

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Answer:

Understand the problem: Understand the problem. $\newline$ We need to evaluate the sum of the expression $(n x + 1)$ for $n$ ranging from $1$ to $3$ . This means we will substitute $n$ with $1$ , $2$ , and $3$ into the expression and sum the results.
Substitute $n = 1$ : Substitute $n = 1$ into the expression and evaluate. $\newline$ For $n = 1$ , the expression becomes $(1x + 1)$ . $\newline$ Calculate the expression for $n = 1$ : $1x + 1 = x + 1$ .
Substitute $n = 2$ : Substitute $n = 2$ into the expression and evaluate. $\newline$ For $n = 2$ , the expression becomes $(2x + 1)$ . $\newline$ Calculate the expression for $n = 2$ : $2x + 1 = 2x + 1$ .
Substitute $n = 3$ : Substitute $n = 3$ into the expression and evaluate. $\newline$ For $n = 3$ , the expression becomes $(3x + 1)$ . $\newline$ Calculate the expression for $n = 3$ : $3x + 1 = 3x + 1$ .
Sum the results: Sum the results from steps $2$ , $3$ , and $4$ . $\newline$ Add the expressions from each step: $(x + 1) + (2x + 1) + (3x + 1)$ . $\newline$ Combine like terms: $x + 2x + 3x + 1 + 1 + 1 = 6x + 3$ .