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9966 [12]
3 years ago
6

Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.

Mathematics
1 answer:
Aleks [24]3 years ago
5 0

Answer:

It means \sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6} also converges.

Step-by-step explanation:

The actual Series is::

\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}

The method we are going to use is comparison method:

According to comparison method, we have:

\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}

\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}

Now:

\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty}  \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

\sum_{n=1}^{inf}\frac{1}{n^p}

if p>1 then series converges. In oue case we have:

\sum_{n=1}^{inf}b_n=\frac{1}{n^4}

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means \sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6} also converges.

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Answer:

11.) 10w^2 + 43w + 21.

12.) -15y^2 - 2y + 8

Check the explanation for details

Step-by-step explanation:

11.) You are meant to multiply each row by both columns. For instance, multiply 5w by 2w and 7 you will get 10 w^2 and 35 w

Also, multiply 3 by both 2w and 7 you will get 6w and 21. Therefore,

Expansion of ( 5w + 3 )( 2w + 7 ) will produce 10w^2 + 37w + 6w + 21

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12.) Repeat the same process by multiplying row by column.

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4 0
3 years ago
Definitions given.
Yuki888 [10]

The pitch of the roof is given by the ratio of the rise to the run of the roof, which is the slope of the rafter

The \ pitch  \ of  \ the \  roof  \ is \ \mathbf {\dfrac{6}{13}}

Please find attached the simple <u>diagram of the house</u> with all measurements labeled

The reason the above value for the pitch and the diagram are correct are as follows:

The given parameters are;

Width of the section of the house on which the gable of the roof is to be placed = 50 feet

Length of the over hang on the sides of the roof = 1 foot each

Total span of the roof = 52 feet

Horizontal length of each rafter, the run = 26 feet

The height of the ridge above the top of the frame, the rise = 12 feet

Required:

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Solution:

Pitch = \dfrac{Rise}{Run}

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Please find attached the <u>diagram</u> of the house showing the measurements for the roof parameters and the section of the house where the gable roof is to be placed

Learn more about finding the slope of a line here:

brainly.com/question/18990889

brainly.com/question/17105217

brainly.com/question/20987659

8 0
2 years ago
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Answer:

<h2><u><em>D</em></u></h2>

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fasle

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