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3 years ago

Determine the rate of change for the data in the table below. Write The rate as a unit rate.

Mathematics

1 answer:

Sladkaya [172]3 years ago

4 0

Answer:

2/6

Step-by-step explanation:

I'm not sure if it's this but there is 2 more balloons added to the left column and 6 more added to the right column.

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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

3 years ago

if a rectangle's length is 2 x − 1 and the width is 4 x − 2 , write an expression for the perimeter and an expression for the ar

miskamm [114]

Answer:

Step-by-step explanation:

2p/2 = 2x+7

1) 2x+7 -x - 5 =

width = x + 2

2) 2p/2 = 21 in

x + 5 + x + 2 = 21

2x = 14

x = 7

lenght = 7 + 5 = 12 in

width = 7 + 2 = 9 in

3 )

A = (x+5)(x+2)

A = 12 x 9 = 108

6 0

2 years ago

Someone plz help this is due today

-Dominant- [34]

3x+5x+1=17

x=2

y=5•2+1

y=1

(x, y)=(2, 11)

3x+2(4x+5)=43

x=3

y=4•3+5

y=17

(x, y)=(3, 17)

I think I did it right and I hope I helped you

3 0

3 years ago

Complete the table. Will choose brainliest.

TEA [102]

Answer:

At starting percentage without tusk is 2.4% and with tusk is 97.6%.At end percentage without tusk is 14.6% and with tusk is 85.3%

4 0

3 years ago

What is the answer to 2(x÷6)?

Jet001 [13]

Answer:

2x÷ 12

Step-by-step explanation:

Use the trick of shaking everybodys hand

2*x=2x

2*6=12

8 0

3 years ago