Find the sigma notation of the following sum:
[tex][(\frac{2}{n})^3-\frac{2}{n} ](\frac{2}{n} )+...+[(\frac{2n}{n} )^3-\frac{2n}{n} ](\frac{2}{n} )[/tex]

Answers

Answer 1

Answer:

[tex]\displaystyle \frac{2}{n} \sum_{i = 1}^{n} \left(\left(\frac{2i}{n}\right)^3 - \frac{2i}{n}\right)[/tex]

Step-by-step explanation:

We have the sum:

[tex]\displaystyle \left[\left(\frac{2}{n}\right)}^3-\frac{2}{n}\right]\left(\frac{2}{n}\right)+...+\left[ \left(\frac{2n}{n}\right)^3-\frac{2n}{n}\right]\left(\frac{2}{n}\right)[/tex]

And we want to find the sigma notation that represents the sum.

Note that the leftmost term is the first term while the rightmost term is the last term.

n is the number of terms. Therefore, (2 / n) will stay constant. Hence, we can factor it out of the series:

[tex]\displaystyle =\frac{2}{n}\left(\left[\left(\frac{2}{n}\right)^3-\frac{2}{n}\right]+...+\left[\left(\frac{2n}{n}\right)^3-\frac{2n}{n}\right]\right)[/tex]

Notice the differences between the first term and the last term. The first term is given by [tex]\displaystyle \left(\frac{2}{n}\right)^3- \frac{2}{n}[/tex]. The last term is given by  [tex]\displaystyle \left(\frac{2n}{n}\right)^3- \frac{2n}{n}[/tex]. Because at the last term, our initial term i is equal to n, we can replace the extra n with i for our summation.

Therefore, we can write the following summation:

[tex]=\displaystyle \sum_{i=1}^{n} \frac{2}{n}\left(\left[\left(\frac{2i}{n}\right)^3-\frac{2i}{n}\right]\right)[/tex]

And since (2 / n) is constant:

[tex]\displaystyle = \frac{2}{n} \sum_{i = 1}^{n} \left(\left(\frac{2i}{n}\right)^3 - \frac{2i}{n}\right)[/tex]


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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

80 + (-36) = 44

The negative in the 36 allows it to be subtracted from 80

Answer:

80 + -36

Step-by-step explanation:

80 - 44 = 36

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O D. (2,-4)

Answers

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(1, -2) is the coordinates that exists on the line y = 2x - 4

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

see the attached for domainRange: (-∞, 4], [3, ∞), [-3, 1]

Step-by-step explanation:

The domain is the horizontal extent of the graph. When the graph has arrows on the end, it extends to infinity in the indicated direction.

__

The range is the vertical extent of the graph.

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__

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__

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Answers

Hello!

We can say that:

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Let's go!

Calculate x, knowing that angles opposite the vertex have the same value: ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓

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To know the value of y, just calculate when the angle 4x - 21 ° is worth, as we already have the value of x. Then just do another equation.

4.14 - 2156 - 21 35

Now, we calculate:

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Now, we calculate z:

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Is important stand out what the draw isn't in the correct scale.

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Step-by-step explanation:

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Answer:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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and PS I am in 7th grade I tried my best and do you want to be friends ? my name is Ayden Hickle.

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Answers

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

41, 7

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Step-by-step explanation:

41, 3+12+6 ÷3

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Answers

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Answer:

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Step-by-step explanation:

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