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3 years ago

Simplify 8+5h-2+h-10+3h

Mathematics

2 answers:

postnew [5]3 years ago

8 0

Answer:

9h-4

Step-by-step explanation:

8+5h-2+h-10+3h

-4+5h+h+3h

Bogdan [553]3 years ago

4 0

Answer:

-4+7h

Step-by-step explanation:

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3 years ago

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.

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3 years ago

andre has 4 times as many model cars as Peter , and Peter has one-third as many model cars as jade . andre has 36 model cars . a

lorasvet [3.4K]

P = how many cars Peter has
j = how many cars Jade has
a = how many cars Andre has
p x 4 = how many cars Andre has (36 model cars)
>>>TO FIND HOW MANY MODEL CARS PETER HAS:
p x 4 = 36
36 / 4 = 9
your equation to find how many model cars Peter has is:
36 / 4 = 9
So, Peter has 9 model cars.
>>>TO FIND HOW MANY MODEL CARS JADE HAS:
36 / 4 = how many cars Peter has (9)
Now, you are given the info that Jade has THREE TIMES (3x) as many cars as Peter already.
So, your equation for this one is:
9 x 3 = 27
So Jade has 27 model cars.

---- Jade has 27 model cars.
---- Andre has 36 model cars.
---- Peter has 9 model cars.

equation for a. 36 / 4 = p
equation for b. 9 x 3 = j

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Maksim231197 [3]

It can't be simplified since 29 is a prime number EDIT: it cant be simplified into whole numbers lol

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