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Evaluate:

sum_(n=0)^(4)(4x+n)
Answer:

Evaluate: $\newline$ $\sum_{n=0}^{4}(4 x+n)$ $\newline$ Answer:

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Evaluate definite integrals using the chain rule

Full solution

Q. Evaluate:

\newline

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

\newline

Answer:

Write Series Terms: Write down the series to be summed. $\newline$ The series is $\sum_{n=0}^{4}(4x+n)$ , which means we need to add together the terms $4x+0$ , $4x+1$ , $4x+2$ , $4x+3$ , and $4x+4$ .
Calculate Series Sum: Calculate the sum of the series. $\newline$ To find the sum, we add all the terms together: $\newline$ $(4x+0) + (4x+1) + (4x+2) + (4x+3) + (4x+4)$ $\newline$ $= 4x + 4x + 4x + 4x + 4x + (0 + 1 + 2 + 3 + 4)$ $\newline$ $= 20x + (0 + 1 + 2 + 3 + 4)$
Simplify Constant Sum: Simplify the constant part of the sum. $\newline$ We add the numbers $0$ through $4$ : $\newline$ $0 + 1 + 2 + 3 + 4 = 10$
Combine $X$ and Constant: Combine the $x$ terms with the constant sum. $\newline$ Now we combine the sum of the $x$ terms with the sum of the constants: $\newline$ $20x + 10$

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