Evaluate the summation below. 7sum_(k=3)^(6)(6k-k^(2)) Answer:

Simplify Expression: Simplify the expression inside the summation 7(6k - k^2). This simplifies to 42k - 7k^2.Distribute Summation: Distribute the summation from k=3 to k=6 into 42k - 7k^2. This gives us sum_(k=3)^(6)42k - sum_(k=3)^(6)7k^2.Evaluate First Term: Evaluate the first term sum_(k=3)^(6)42k. This is a sum of a linear sequence, which can be calculated by adding the terms directly. sum_(k=3)^(6)42k = 42*3 + 42*4 + 42*5 + 42*6 = 126 + 168 + 210 + 252 = 756Evaluate Second Term: Evaluate the second term sum_(k=3)^(6)7k^2. This is a sum of squares, which can also be calculated by adding the terms directly. sum_(k=3)^(6)7k^2 = 7*3^2 + 7*4^2 + 7*5^2 + 7*6^2 = 63 + 112 + 175 + 252 = 602Subtract Sums: Subtract the second sum from the first sum to get the final answer. Final Answer = 756 - 602 = 154

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Evaluate the summation below.

7sum_(k=3)^(6)(6k-k^(2))
Answer:

Evaluate the summation below. $\newline$ $7 \sum_{k=3}^{6}\left(6 k-k^{2}\right)$ $\newline$ Answer:

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Algebra 2

Sum of finite series starts from 1

Full solution

Q. Evaluate the summation below.

\newline

7 \sum_{k=3}^{6}\left(6 k-k^{2}\right)

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Answer:

Simplify Expression: Simplify the expression inside the summation $7(6k - k^2)$ . This simplifies to $42k - 7k^2$ .
Distribute Summation: Distribute the summation from $k=3$ to $k=6$ into $42k - 7k^2$ . This gives us $\sum_{k=3}^{6}42k - \sum_{k=3}^{6}7k^2$ .
Evaluate First Term: Evaluate the first term $\sum_{k=3}^{6}42k$ . This is a sum of a linear sequence, which can be calculated by adding the terms directly. $\sum_{k=3}^{6}42k = 42\times 3 + 42\times 4 + 42\times 5 + 42\times 6 = 126 + 168 + 210 + 252 = 756$
Evaluate Second Term: Evaluate the second term $\sum_{k=3}^{6}7k^2$ . This is a sum of squares, which can also be calculated by adding the terms directly. $\sum_{k=3}^{6}7k^2 = 7\cdot3^2 + 7\cdot4^2 + 7\cdot5^2 + 7\cdot6^2 = 63 + 112 + 175 + 252 = 602$
Subtract Sums: Subtract the second sum from the first sum to get the final answer. $\newline$ Final Answer = $756 - 602$ $\newline$ = $154$