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2 years ago

Tell whether the given value is a solution for the inequality. Then, justify your answer.

Mathematics

1 answer:

tatuchka [14]2 years ago

4 0

Answer:

x=18 is not a solution

Step-by-step explanation:

18+9=27 but this is saying it has to be less than 27 so this is not a solution

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Consider the series ∑n=1[infinity]2nn!nn. Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it d

Vikki [24]

I guess the series is

$\displaystyle\sum_{n=1}^\infty\frac{2^nn!}{n^n}$

We have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{2^{n+1}(n+1)!}{(n+1)^{n+1}}}{\frac{2^nn!}{n^n}}\right|=2\lim_{n\to\infty}\left(\frac n{n+1}\right)^n$

Recall that

$e=\displaystyle\lim_{n\to\infty}\left(1+\frac1n\right)^n$

In our limit, we have

$\dfrac n{n+1}=\dfrac{n+1-1}{n+1}=1-\dfrac1{n+1}$

$\left(\dfrac n{n+1}\right)^n=\dfrac{\left(1-\frac1{n+1}\right)^{n+1}}{1-\frac1{n+1}}$

$\implies\displaystyle2\lim_{n\to\infty}\left(\frac n{n+1}\right)^n=2\frac{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)^{n+1}}{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)}=\frac{2e}1=2e$

which is greater than 1, which means the series is divergent by the ratio test.

On the chance that you meant to write

$\displaystyle\sum_{n=1}^\infty\frac{2^n}{n!n^n}$

we have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{2^{n+1}}{(n+1)!(n+1)^{n+1}}}{\frac{2^n}{n!n^n}}\right|=2\lim_{n\to\infty}\frac1{(n+1)^2}\left(\frac n{n+1}\right)^2$

$=\displaystyle2\left(\lim_{n\to\infty}\frac1{(n+1)^2}\right)\left(\lim_{n\to\infty}\left(\frac n{n+1}\right)^n\right)=2\cdot0\cdot e=0$

which is less than 1, so this series is absolutely convergent.

6 0

2 years ago

What are the solutions of the quadratic equation?

Cloud [144]

We have x^2 + 2 · x · (11/2) + (11/2)^2 = - 24 + (11/2)^2;
Then, ( x + 11/2 )^2 = -24 + 121/4;
( x + 11/2 )^2 + 96/4 - 121/4 = 0;
( x + 11/2 )^2 - 25 / 4 = 0;
( x + 11/2 )^2 - (5/2)^2 = 0;
( x + 11/2 - 5/2)·( x + 11/2 + 5/2 ) = 0;
( x + 6/2 )·( x + 16/2 ) = 0;
( x + 3 )· ( x + 8 ) = 0;
x = - 3 or x = -8;
The first choice is the correct answer.

8 0

2 years ago

Read 2 more answers

3T= _______lbs

sveticcg [70]

Answer:

Step-by-step explanation:

Hope it is helpful...

3 0

2 years ago

What is not equivalent to 36/72

STALIN [3.7K]

Any fraction that does not equal 1/2.

6 0

2 years ago

Chris has 150 cookies to sell each cookie is covered with one topping 1 /5 of cookie are covered with coconut 1/3 of the cookie

Elan Coil [88]

Answer:

1/6 or 25

Step-by-step explanation:

1/3=10/30

3/10=9/30

1/5=6/30

together is 25/30, which leaves the rest, 5/30 or 1/6 or 25 cookies.

3 0

3 years ago