Evaluate: sum_(n=1)^(4)(nx-1) Answer:

Write Terms Explicitly: Write out the terms of the series explicitly. The series is sum_(n=1)^(4)(nx-1), which means we add up the terms (nx-1) for each value of n from 1 to 4. So the terms are: (1x-1) + (2x-1) + (3x-1) + (4x-1)Combine Like Terms: Combine like terms. We can combine the x terms and the constant terms separately. (1x + 2x + 3x + 4x) - (1 + 1 + 1 + 1) This simplifies to: 10x - 4Check for Errors: Check for any mathematical errors. There are no mathematical errors in the previous steps. The terms were combined correctly, and the like terms were added together properly.Write Final Answer: Write the final answer. The sum of the series from n=1 to 4 of the expression (nx-1) is 10x - 4.

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Evaluate: $\newline$ $\sum_{n=1}^{4}(n x-1)$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the chain rule

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Q. Evaluate:

\newline

\sum_{n=1}^{4}(n x-1)

\newline

Answer:

Write Terms Explicitly: Write out the terms of the series explicitly. $\newline$ The series is $\sum_{n=1}^{4}(nx-1)$ , which means we add up the terms $(nx-1)$ for each value of $n$ from $1$ to $4$ . $\newline$ So the terms are: $\newline$ $(1x-1) + (2x-1) + (3x-1) + (4x-1)$
Combine Like Terms: Combine like terms. $\newline$ We can combine the $x$ terms and the constant terms separately. $\newline$ $(1x + 2x + 3x + 4x) - (1 + 1 + 1 + 1)$ $\newline$ This simplifies to: $\newline$ $10x - 4$
Check for Errors: Check for any mathematical errors. $\newline$ There are no mathematical errors in the previous steps. The terms were combined correctly, and the like terms were added together properly.
Write Final Answer: Write the final answer. $\newline$ The sum of the series from $n=1$ to $4$ of the expression $(nx-1)$ is $10x - 4$ .