Evaluate the summation below. 3sum_(m=0)^(4)(2m^(2)-6) Answer:

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Evaluate the summation below.  3sum_(m=0)^(4)(2m^(2)-6) Answer:

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Understand Summation Notation: First, we need to understand the summation notation. The expression 3∑(from m=0 to 4) of (2m^2 - 6) means that we will substitute m with each integer from 0 to 4 into the expression (2m^2 - 6), sum all the resulting values, and then multiply the sum by 3.Substitute m=0: Let's start by substituting m=0 into the expression (2m^2 - 6). This gives us 2(0)^2 - 6, which simplifies to 0 - 6, resulting in -6.Substitute m=1: Next, substitute m=1 into the expression (2m^2 - 6). This gives us 2(1)^2 - 6, which simplifies to 2 - 6, resulting in -4.Substitute m=2: Now, substitute m=2 into the expression (2m^2 - 6). This gives us 2(2)^2 - 6, which simplifies to 2(4) - 6, resulting in 8 - 6, which is 2.Substitute m=3: Substitute m=3 into the expression (2m^2 - 6). This gives us 2(3)^2 - 6, which simplifies to 2(9) - 6, resulting in 18 - 6, which is 12.Substitute m=4: Finally, substitute m=4 into the expression (2m^2 - 6). This gives us 2(4)^2 - 6, which simplifies to 2(16) - 6, resulting in 32 - 6, which is 26.Add Substitution Results: Now, we add all the values obtained from the substitutions: -6 + (-4) + 2 + 12 + 26. This results in a sum of 30.Multiply by 3: The last step is to multiply the sum by 3, as indicated by the expression 3∑. So we calculate 3 * 30, which equals 90.

Evaluate the summation below. $\newline$ $3 \sum_{m=0}^{4}\left(2 m^{2}-6\right)$ $\newline$ Answer:

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Evaluate the summation below. $\newline$ $3 \sum_{m=0}^{4}\left(2 m^{2}-6\right)$ $\newline$ Answer: