Evaluate: sum_(n=2)^(6)(nx+3) Answer:

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Evaluate:  sum_(n=2)^(6)(nx+3) Answer:

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Understand the problem: Understand the problem. We need to evaluate the sum of the expression (nx + 3) for each integer value of n from 2 to 6. This means we will substitute n with each of the integers from 2 to 6, calculate the expression for each, and then add all the results together.Substitute n = 2: Substitute n = 2 into the expression and calculate. For n = 2, the expression becomes (2x + 3).Substitute n = 3: Substitute n = 3 into the expression and calculate. For n = 3, the expression becomes (3x + 3).Substitute n = 4: Substitute n = 4 into the expression and calculate. For n = 4, the expression becomes (4x + 3).Substitute n = 5: Substitute n = 5 into the expression and calculate. For n = 5, the expression becomes (5x + 3).Substitute n = 6: Substitute n = 6 into the expression and calculate. For n = 6, the expression becomes (6x + 3).Add all the expressions together: Add all the expressions together. Now we add the expressions from steps 2 to 6: (2x + 3) + (3x + 3) + (4x + 3) + (5x + 3) + (6x + 3).Combine like terms: Combine like terms. We combine the x terms and the constant terms separately: (2x + 3x + 4x + 5x + 6x) + (3 + 3 + 3 + 3 + 3).Perform the addition: Perform the addition. Adding the x terms: 2x + 3x + 4x + 5x + 6x = 20x. Adding the constant terms: 3 + 3 + 3 + 3 + 3 = 15.Write the final result: Write the final result. The sum of the expression from n = 2 to 6 is 20x + 15.

Evaluate: $\newline$ $\sum_{n=2}^{6}(n x+3)$ $\newline$ Answer:

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Evaluate: $\newline$ $\sum_{n=2}^{6}(n x+3)$ $\newline$ Answer: