Evaluate: sum_(n=0)^(2)(nx+1) Answer:

Evaluate Expression Range: We are asked to evaluate the sum of the expression (nx + 1) for n ranging from 0 to 2. This is a finite series where we substitute the values of n into the expression and sum the results.Substitute n = 0: First, substitute n = 0 into the expression (nx + 1). This gives us (0*x + 1), which simplifies to 1.Substitute n = 1: Next, substitute n = 1 into the expression (nx + 1). This gives us (1*x + 1), which simplifies to (x + 1).Substitute n = 2: Finally, substitute n = 2 into the expression (nx + 1). This gives us (2*x + 1), which simplifies to (2x + 1).Sum Substitutions: Now, sum the results of the substitutions: 1 + (x + 1) + (2x + 1).Combine Like Terms: Combine like terms: 1 + x + 1 + 2x + 1 = 3 + 3x.

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Algebra 2

Simplify variable expressions using properties

Full solution

Q. Evaluate:

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\sum_{n=0}^{2}(n x+1)

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Answer:

Evaluate Expression Range: We are asked to evaluate the sum of the expression $n x + 1$ for $n$ ranging from $0$ to $2$ . This is a finite series where we substitute the values of $n$ into the expression and sum the results.
Substitute $n = 0$ : First, substitute $n = 0$ into the expression $(nx + 1)$ . This gives us $(0\times x + 1)$ , which simplifies to $1$ .
Substitute $n = 1$ : Next, substitute $n = 1$ into the expression $(nx + 1)$ . This gives us $(1\times x + 1)$ , which simplifies to $(x + 1)$ .
Substitute $n = 2$ : Finally, substitute $n = 2$ into the expression $(n\times x + 1)$ . This gives us $(2\times x + 1)$ , which simplifies to $(2x + 1)$ .
Sum Substitutions: Now, sum the results of the substitutions: $1 + (x + 1) + (2x + 1)$ .
Combine Like Terms: Combine like terms: $1 + x + 1 + 2x + 1 = 3 + 3x$ .