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

Substitute n with 2: For n=2, substitute n with 2 in the expression (nx-3): 2x - 3Substitute n with 3: For n=3, substitute n with 3 in the expression (nx-3): 3x - 3Substitute n with 4: For n=4, substitute n with 4 in the expression (nx-3): 4x - 3Substitute n with 5: For n=5, substitute n with 5 in the expression (nx-3): 5x - 3Substitute n with 6: For n=6, substitute n with 6 in the expression (nx-3): 6x - 3Add all terms together: Now, add all the terms together: (2x - 3) + (3x - 3) + (4x - 3) + (5x - 3) + (6x - 3) Combine like terms by adding the coefficients of x together and the constant terms together: (2x + 3x + 4x + 5x + 6x) - (3 + 3 + 3 + 3 + 3)Combine like terms: Calculate the sum of the coefficients of x: 2x + 3x + 4x + 5x + 6x = 20xCalculate sum of coefficients: Calculate the sum of the constant terms: 3 + 3 + 3 + 3 + 3 = 15Calculate sum of constants: Subtract the sum of the constant terms from the sum of the coefficients of x: 20x - 15 This is the simplified form of the sum expression.

Home

Math Problems

Algebra 2

Evaluate rational expressions II

Full solution

Q. Evaluate:

\newline

\sum_{n=2}^{6}(n x-3)

\newline

Answer:

\newline

Submit Answer

Substitute $n$ with $2$ : For $n=2$ , substitute $n$ with $2$ in the expression $(nx-3)$ : $2x - 3$
Substitute $n$ with $3$ : For $n=3$ , substitute $n$ with $3$ in the expression $(nx-3)$ : $3x - 3$
Substitute $n$ with $4$ : For $n=4$ , substitute $n$ with $4$ in the expression $(nx-3)$ : $4x - 3$
Substitute $n$ with $5$ : For $n=5$ , substitute $n$ with $5$ in the expression $(nx-3)$ : $5x - 3$
Substitute $n$ with $6$ : For $n=6$ , substitute $n$ with $6$ in the expression $(nx-3)$ : $6x - 3$
Add all terms together: Now, add all the terms together: $\newline$ $(2x - 3) + (3x - 3) + (4x - 3) + (5x - 3) + (6x - 3)$ $\newline$ Combine like terms by adding the coefficients of $x$ together and the constant terms together: $\newline$ $(2x + 3x + 4x + 5x + 6x) - (3 + 3 + 3 + 3 + 3)$
Combine like terms: Calculate the sum of the coefficients of $x$ : $2x + 3x + 4x + 5x + 6x = 20x$
Calculate sum of coefficients: Calculate the sum of the constant terms: $3 + 3 + 3 + 3 + 3 = 15$
Calculate sum of constants: Subtract the sum of the constant terms from the sum of the coefficients of $x$ : $20x - 15$ This is the simplified form of the sum expression.