Evaluate the summation below. sum_(n=0)^(4)(6n^(2)-8n) Answer:

Identify series and range: Identify the series to be summed and the range of the summation. We are given the series 6n^2 - 8n and we need to sum it from n=0 to n=4.Evaluate series at each n: Evaluate the series at each value of n from 0 to 4 and sum the results. For n=0: 6(0)^2 - 8(0) = 0 For n=1: 6(1)^2 - 8(1) = 6 - 8 = -2 For n=2: 6(2)^2 - 8(2) = 24 - 16 = 8 For n=3: 6(3)^2 - 8(3) = 54 - 24 = 30 For n=4: 6(4)^2 - 8(4) = 96 - 32 = 64 Now, sum these results: 0 + (-2) + 8 + 30 + 64.Perform addition to find sum: Perform the addition to find the sum of the series. 0 + (-2) + 8 + 30 + 64 = 0 - 2 + 8 + 30 + 64 = 100

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Evaluate the summation below.

sum_(n=0)^(4)(6n^(2)-8n)
Answer:

Evaluate the summation below. $\newline$ $\sum_{n=0}^{4}\left(6 n^{2}-8 n\right)$ $\newline$ Answer:

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Algebra 2

Sum of finite series starts from 1

Full solution

Q. Evaluate the summation below.

\newline

\sum_{n=0}^{4}\left(6 n^{2}-8 n\right)

\newline

Answer:

Identify series and range: Identify the series to be summed and the range of the summation. $\newline$ We are given the series $6n^2 - 8n$ and we need to sum it from $n=0$ to $n=4$ .
Evaluate series at each n: Evaluate the series at each value of $n$ from $0$ to $4$ and sum the results. $\newline$ For $n=0$ : $6(0)^2 - 8(0) = 0$ $\newline$ For $n=1$ : $6(1)^2 - 8(1) = 6 - 8 = -2$ $\newline$ For $n=2$ : $6(2)^2 - 8(2) = 24 - 16 = 8$ $\newline$ For $n=3$ : $0$ $0$ $\newline$ For $0$ $1$ : $0$ $2$ $\newline$ Now, sum these results: $0$ $3$ .
Perform addition to find sum: Perform the addition to find the sum of the series. $\newline$ $0 + (-2) + 8 + 30 + 64 = 0 - 2 + 8 + 30 + 64 = 100$