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AlekseyPX
3 years ago
14

Use the Ratio Test to determine whether the series is convergent or divergent. [infinity] n! 112n n = 1 Identify an. Correct: Yo

ur answer is correct. Evaluate the following limit. lim n → [infinity] an + 1 an Since lim n → [infinity] an + 1 an 1,
Mathematics
1 answer:
MakcuM [25]3 years ago
7 0

Answer:

Step-by-step explanation:

Recall that the ratio test is stated as follows:

Given a series of the form \sum_{n=1}^{\infty} a_n let L=\lim_{n\to \infty}\left|\frac{a_{n+1}}{a_n}\right|

If L<1, then the series converge absolutely, if L>1, then the series diverge. If L fails to exist or L=1, then the test is inconclusive.

Consider the given series \sum_{n=1}^{\infty} n! \cdot 112n. In this case, a_n =n! \cdot 112n, so , consider the limit

\lim_{n\to\infty} \frac{(n+1)! 112 (n+1)}{n! 112 n} = \lim_{n\to\infty}\frac{(n+1)^2}{n}

Since the numerator has a greater exponent than the numerator, the limit is infinity, which is greater than one, hence, the series diverge by the ratio test

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The volume of Saturn is about 8.27 x 10 cubic kilometers. The volume of Earth is about 1.09 x 102 cubic kilometers. The number o
ivann1987 [24]

Answer:

Option D: 7.59*10^{2}

Step-by-step explanation:

we know that

The volume of Saturn is about 8.27*10^{14}\ km^{3}

The volume of Earth is about 1.09*10^{12}\ km^{3}

Dividing Saturn's volume by Earth's volume

\frac{8.27*10^{14}}{1.09*10^{12}} =(\frac{8.27}{1.09})*10^{14-12} =7.59*10^{2}

4 0
2 years ago
3x+2(4x-4)=3 help pls
Vlada [557]

Answer: 1

Step-by-step explanation:

3x + 8x-8= 3

11x-8=3

Then you move the 8 to the other side and change it to a positive.

11x= 11

11x/11 = 11/11

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2 years ago
Divide 12x^4+17^3+8x-40 by x-2
chubhunter [2.5K]

Answer:

12x^3 + 24x^2 + 48x + 104 + (5081/x-2)

Step-by-step explanation:

12x^4 + 17* (17*17) + 8x -40/ x-2

1. remove the parenthesis

12x^4 + !7 * 17 * 17 + 8x -40 / x-2

2. multiply 17 by 17

12x^4 + 289 * 17 + 8x -= 40 /x-2

3. multiply 289 by 17

12x^ = 4913 + 8x - 40 / x-2

4. move 4913

12x^4 + 8x + 4913 - 40 / x-2

5. subtract 40 from 4913

12x^4 + 8x + 4873 / x-2

6. set up polynomials to be divided. if there is not a term for every exponent, insert one with a value of 0

x-2 into 12x^4 + 0x^3 + 0x^2 + 8x + 4873

7. divide the highest order term  in the dividend 12x^4 by the highest order term in divisor x = 12x^3

8. multiply by new quotient term

12x^3 * x-2 = 12x^4 -24x^3

9. the expression needs to be subtracted from the dividend, so change all the signs in 12x^4 - 24x^3

12x^4 + 0x^3 - 12x^4 + 24x^3

10. after changing the signs, add the last dividend from the multiplied polynomial to find new dividend

+24x^3

11.  pull the next term from the original dividend down into the current dividend

+24x^3 + 0x^2

12.  divide the highest order term in the dividend 24x^3 by the highest order term in divisor x = 24x^2

12x^3 + 24x^2

13. multiply new quotient by the divisor

24x^3 * x-2 = 24x^3 - 48x^2

14. the expression needs to be subtracted from the dividend, so change all the signs in 24x^3 - 48x^2

24x^3 + 0x^2 - 24x^3 + 48x^2

15. after changing the signs, add the last dividend from the multiplied polynomial to find new dividend

+48x^2

16. pull the next terms from the original dividend down to the current dividend

+ 48x^2 + 8x

17. divide the highest order term in the dividend 48x^2 by the highest order term in the divisor = 48x

12x^3 + 24x^2 + 48x

18. multiply the new quotient term by the divisor

48x * x - 2 = 48x^2 - 96x

19. the expression needs to be subtracted from the dividend, so change all the signs in 48x^2 - 96x

-48x^2 + 96x

20. after changing the signs, add the last dividend from the multiplied polynomial to find new dividend

48x^2 + 8x - 48x^2 + 96x

= 104x

21. pull the next terms from the original dividend down to the current dividend

+ 104x + 4873

22. divide the highest order term in the dividend 104x by the highest order term in the divisor x = 104

23. divide the new quotient by the divisor

104 * x -2 = 104x - 208

24. the expression needs to be subtracted from the dividend, so change all the signs in 104x - 208

104x + 4873 - 104x + 208 = 5081

25. the final answer is the quotient plus the remainder over the divisor

12x^3 + 24x^2 + 48x + 104 + (5081 / x - 2)

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3 years ago
Solve for x. Round your answer to the nearest tenth if necessary.
eduard

Answer: 15.9

Step-by-step explanation:

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