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

Write Series Expression: Write down the series to be evaluated. We need to evaluate the summation of the series given by the expression 2 * sum from i equals 0 to 3 of (3i - 3i^2). This means we will calculate the sum for each value of i from 0 to 3, multiply each term by 2, and then add up all the terms.Calculate Series Terms: Calculate the terms of the series for each value of i. For i = 0: 2 * (3*0 - 3*0^2) = 2 * (0 - 0) = 0 For i = 1: 2 * (3*1 - 3*1^2) = 2 * (3 - 3) = 0 For i = 2: 2 * (3*2 - 3*2^2) = 2 * (6 - 12) = -12 For i = 3: 2 * (3*3 - 3*3^2) = 2 * (9 - 27) = -36Add Terms: Add up all the terms calculated in Step 2. Sum = 0 + 0 - 12 - 36 = -48Final Answer: State the final answer. The sum of the series is -48.

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Evaluate the summation below.

2sum_(i=0)^(3)(3i-3i^(2))
Answer:

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

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Algebra 2

Sum of finite series starts from 1

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Q. Evaluate the summation below.

\newline

2 \sum_{i=0}^{3}\left(3 i-3 i^{2}\right)

\newline

Answer:

Write Series Expression: Write down the series to be evaluated. $\newline$ We need to evaluate the summation of the series given by the expression $2 \times \sum_{i=0}^{3} (3i - 3i^2)$ . This means we will calculate the sum for each value of $i$ from $0$ to $3$ , multiply each term by $2$ , and then add up all the terms.
Calculate Series Terms: Calculate the terms of the series for each value of $i$ .
For $i = 0$ : $2 \times (3\times0 - 3\times0^2) = 2 \times (0 - 0) = 0$
For $i = 1$ : $2 \times (3\times1 - 3\times1^2) = 2 \times (3 - 3) = 0$
For $i = 2$ : $2 \times (3\times2 - 3\times2^2) = 2 \times (6 - 12) = -12$
For $i = 3$ : $2 \times (3\times3 - 3\times3^2) = 2 \times (9 - 27) = -36$
Add Terms: Add up all the terms calculated in Step $2$ . $\newline$ Sum = $0 + 0 - 12 - 36 = -48$
Final Answer: State the final answer. $\newline$ The sum of the series is $-48$ .