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Shkiper50 [21]
3 years ago
8

I will give brainliest if you answer all correctly ​

Mathematics
1 answer:
miskamm [114]3 years ago
7 0

Answer:

I think 13 is C

Step-by-step explanation:

71+52= 123

180-123= 57

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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.

5 0
3 years ago
Solve this simultaneous equation x+2y=11 <br> x-2y=1
lana [24]

Answer:

Equation 1,

x + 2y = 11

Equation 2,

x - 2y = 11

Take equation number 2.

x  -  2y = 11 \\ x = 11  +  2y

Substitute 'x' in Equation number 1.

x + 2y = 11 \\ 11 + 2y + 2y = 11 \\ 11 + 4y = 11 \\ 4y = 11 - 11 \\ 4y = 0 \\ y =  \frac{0}{4}  \\ y = 0

<u>y = 0.</u>

So x,

x = 11 - 2y \\ x = 11 - 2(0) \\ x = 11 - 0 \\ x = 11

<u>x = 11.</u>

7 0
3 years ago
Read 2 more answers
A number written in the form a + bi is called a _____ number.
Amiraneli [1.4K]

Answer: A. Complex

Step-by-step explanation: hope this helps!

6 0
2 years ago
Find the area of a patio shaped like the figure shown below with a length of each square equal to one meter. Please answer asap.
Mrrafil [7]

Answer:If my calculations are correct and my rounding I would show you my work but I cant upload the picture but I think about

38

Step-by-step explanation:

I=Hope I helped if so can I please have brainliest :)

6 0
2 years ago
Read 2 more answers
In the topic of mathematical limits, what does converges and diverges mean?
11111nata11111 [884]
In the analysis of an infinite series, the sequence of partial sums are can be classified as either convergent of divergent. The series can be classified as a convergent sequence when a limit exists and is finite. The opposite is true, where the sequence of partial sums can be classified as a divergent sequence when the limit doesn't exist or is positive of negative infinity.
3 0
3 years ago
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