Evaluate the summation below. sum_(i=0)^(3)(-5i^(2)-6i) Answer:

Understand summation notation: Understand the summation notation and the expression to be summed. The summation notation ∑ indicates that we need to sum the expression (-5i^2 - 6i) for each integer value of i starting from 0 and ending at 3.Calculate for i=0: Calculate the expression for i=0. For i=0, the expression (-5i^2 - 6i) becomes (-5*0^2 - 6*0) which simplifies to 0.Calculate for i=1: Calculate the expression for i=1. For i=1, the expression (-5i^2 - 6i) becomes (-5*1^2 - 6*1) which simplifies to (-5 - 6) = -11.Calculate for i=2: Calculate the expression for i=2. For i=2, the expression (-5i^2 - 6i) becomes (-5*2^2 - 6*2) which simplifies to (-5*4 - 12) = -20 - 12 = -32.Calculate for i=3: Calculate the expression for i=3. For i=3, the expression (-5i^2 - 6i) becomes (-5*3^2 - 6*3) which simplifies to (-5*9 - 18) = -45 - 18 = -63.Sum values: Sum the values from steps 2 to 5. Sum = 0 + (-11) + (-32) + (-63) Sum = -11 - 32 - 63 Sum = -106

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Find derivatives of using multiple formulae

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Q. Evaluate the summation below.

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\sum_{i=0}^{3}\left(-5 i^{2}-6 i\right)

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Answer:

Understand summation notation: Understand the summation notation and the expression to be summed. $\newline$ The summation notation $\sum$ indicates that we need to sum the expression $(-5i^2 - 6i)$ for each integer value of $i$ starting from $0$ and ending at $3$ .
Calculate for $i=0$ : Calculate the expression for $i=0$ . For $i=0$ , the expression $(-5i^2 - 6i)$ becomes $(-5\cdot 0^2 - 6\cdot 0)$ which simplifies to $0$ .
Calculate for $i=1$ : Calculate the expression for $i=1$ . For $i=1$ , the expression $(-5i^2 - 6i)$ becomes $(-5\cdot1^2 - 6\cdot1)$ which simplifies to $(-5 - 6) = -11$ .
Calculate for $i=2$ : Calculate the expression for $i=2$ . For $i=2$ , the expression $(-5i^2 - 6i)$ becomes $(-5\cdot2^2 - 6\cdot2)$ which simplifies to $(-5\cdot4 - 12) = -20 - 12 = -32$ .
Calculate for $i=3$ : Calculate the expression for $i=3$ . For $i=3$ , the expression $(-5i^2 - 6i)$ becomes $(-5\cdot3^2 - 6\cdot3)$ which simplifies to $(-5\cdot9 - 18) = -45 - 18 = -63$ .
Sum values: Sum the values from steps $2$ to $5$ . $\newline$ Sum = $0 + (-11) + (-32) + (-63)$ $\newline$ Sum = $-11 - 32 - 63$ $\newline$ Sum = $-106$