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

Understand the problem: Understand the problem. We need to evaluate the sum of the expression (x + n) as n varies from 0 to 2. This means we will substitute n with 0, 1, and 2 into the expression and add the results together.Substitute n = 0: Substitute n = 0 into the expression. When n = 0, the expression (x + n) becomes (x + 0), which simplifies to x.Substitute n = 1: Substitute n = 1 into the expression. When n = 1, the expression (x + n) becomes (x + 1).Substitute n = 2: Substitute n = 2 into the expression. When n = 2, the expression (x + n) becomes (x + 2).Add the results: Add the results from steps 2, 3, and 4. We add x (from step 2), (x + 1) (from step 3), and (x + 2) (from step 4) together: x + (x + 1) + (x + 2).Simplify the expression: Simplify the expression. Combining like terms, we get: x + x + x + 1 + 2 = 3x + 3.

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Find the roots of factored polynomials

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Q. Evaluate:

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

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Answer:

Understand the problem: Understand the problem. $\newline$ We need to evaluate the sum of the expression $(x + n)$ as $n$ varies from $0$ to $2$ . This means we will substitute $n$ with $0$ , $1$ , and $2$ into the expression and add the results together.
Substitute $n = 0$ : Substitute $n = 0$ into the expression. $\newline$ When $n = 0$ , the expression $(x + n)$ becomes $(x + 0)$ , which simplifies to $x$ .
Substitute $n = 1$ : Substitute $n = 1$ into the expression. $\newline$ When $n = 1$ , the expression $(x + n)$ becomes $(x + 1)$ .
Substitute $n = 2$ : Substitute $n = 2$ into the expression. $\newline$ When $n = 2$ , the expression $(x + n)$ becomes $(x + 2)$ .
Add the results: Add the results from steps $2$ , $3$ , and $4$ . $\newline$ We add $x$ (from step $2$ ), $(x + 1)$ (from step $3$ ), and $(x + 2)$ (from step $4$ ) together: $x + (x + 1) + (x + 2)$ .
Simplify the expression: Simplify the expression. $\newline$ Combining like terms, we get: $x + x + x + 1 + 2 = 3x + 3$ .