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3 years ago

Find the volume of 6.3, 7 , 21

Mathematics

1 answer:

RoseWind [281]3 years ago

8 0

Just do 6.3 × 7 × 21. Which is then equal to 926.1^3.

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

Aleks [24]

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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3 years ago

Select all the statements that describe the expression 5 + 2x.

FromTheMoon [43]

It's A that's correct!!!!

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The customer saves $1.65 by using a coupon. The coupon takes 30% off the original price of the cereal. What is the original pric

Ierofanga [76]

The original box was $5.50

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3 years ago

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What is 4/5 as a decimal

Kryger [21]

.8

All percents are out of 100, so to figure out the answer you must make the denominator, or bottom number in your fraction, 100.

To get to 100, you would multiply 5x20, because that equals 100. Because you multiplied the denominator, which is 5, you must multiply the top number by 20 as well.

4x20 = 80

So therefore, the answer is 80/100, so .8

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Simplify <br> Rewrite the expression in the form 4n (4^11)(4^-8)

VARVARA [1.3K]

Answer:

k12

Step-by-step explanation:

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