Evaluate: sum_(n=0)^(4)(nx-5) Answer:

Understand the expression: Understand the expression The expression sum_(n=0)^(4)(nx-5) means we need to calculate the sum of the terms (nx-5) for each integer value of n from 0 to 4.Evaluate n=0: Evaluate the expression for n=0 When n=0, the term is (0*x-5) which simplifies to -5.Evaluate n=1: Evaluate the expression for n=1 When n=1, the term is (1*x-5) which simplifies to x-5.Evaluate n=2: Evaluate the expression for n=2 When n=2, the term is (2*x-5) which simplifies to 2x-5.Evaluate n=3: Evaluate the expression for n=3 When n=3, the term is (3*x-5) which simplifies to 3x-5.Evaluate n=4: Evaluate the expression for n=4 When n=4, the term is (4*x-5) which simplifies to 4x-5.Add all terms: Add all the terms together Now we add all the terms from n=0 to n=4: (-5) + (x-5) + (2x-5) + (3x-5) + (4x-5)Combine like terms: Combine like terms Combine the x terms and the constant terms: (-5) + (-5) + (-5) + (-5) + (-5) + x + 2x + 3x + 4x This simplifies to 10x - 25.Verify final answer: Verify the final answer The final expression 10x - 25 is the sum of the terms (nx-5) from n=0 to n=4.

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Q. Evaluate:

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\sum_{n=0}^{4}(n x-5)

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Answer:

Understand the expression: Understand the expression $\newline$ The expression $\sum_{n=0}^{4}(nx-5)$ means we need to calculate the sum of the terms $(nx-5)$ for each integer value of $n$ from $0$ to $4$ .
Evaluate $n=0$ : Evaluate the expression for $n=0$ When $n=0$ , the term is $(0\times x-5)$ which simplifies to $-5$ .
Evaluate $n=1$ : Evaluate the expression for $n=1$ When $n=1$ , the term is $(1\times x-5)$ which simplifies to $x-5$ .
Evaluate $n=2$ : Evaluate the expression for $n=2$ When $n=2$ , the term is $(2\times x-5)$ which simplifies to $2x-5$ .
Evaluate $n=3$ : Evaluate the expression for $n=3$ When $n=3$ , the term is $(3\times x-5)$ which simplifies to $3x-5$ .
Evaluate $n=4$ : Evaluate the expression for $n=4$ When $n=4$ , the term is $(4\times x-5)$ which simplifies to $4x-5$ .
Add all terms: Add all the terms together $\newline$ Now we add all the terms from $n=0$ to $n=4$ : $\newline$ $(-5) + (x-5) + (2x-5) + (3x-5) + (4x-5)$
Combine like terms: Combine like terms $\newline$ Combine the $x$ terms and the constant terms: $\newline$ $(-5) + (-5) + (-5) + (-5) + (-5) + x + 2x + 3x + 4x$ $\newline$ This simplifies to $10x - 25$ .
Verify final answer: Verify the final answer $\newline$ The final expression $10x - 25$ is the sum of the terms $(nx-5)$ from $n=0$ to $n=4$ .