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Cloud [144]
3 years ago
13

Determine if this series converges or diverges. Find the sum if possible. 250, 50, 10...

Mathematics
2 answers:
Kruka [31]3 years ago
7 0

Answer:

50

Step-by-step explanation:

Elodia [21]3 years ago
3 0

Answer:

312.5

Step-by-step explanation:

We have the series: 250, 50, 10...

As we can see, each subsequent term gets smaller and smaller. Eventually, it will be infinitesimally small. So, our series converges.

We can also see this from our common ratio. Each term is 1/5 of the previous term. Since our r 1/5 is less than 1, our series will converge.

Since it converges, we can indeed find our sum. First, we can write our series using summation. This will be:

\displaystyle{\sum_{n=0}^{\infty} 250(\frac{1}{5})^n }

We can use the following infinite geometric series formula:

\displaystyle{\sum_{n=0}^{\infty} ar^n=\frac{a}{1-r}

So, let's substitute 250 for a and 1/5 for r. This yields:

\displaystyle{\sum_{n=0}^{\infty} 250(\frac{1}{5})^n }=\frac{250}{1-\frac{1}{5}}

Subtract:

\displaystyle{\sum_{n=0}^{\infty} 250(\frac{1}{5})^n }=\frac{250}{\frac{4}{5}}

Divide. So, our series converges to:

\displaystyle{\sum_{n=0}^{\infty} 250(\frac{1}{5})^n }=312.5

And we're done!

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What is the inverse of the function f(x) = x – 12?
Luda [366]

Answer:a


Step-by-step explanation:

h(x)=x-12

h(x)=4x-48

h(x)=-1(4x-48)

h(x)=-4x+48

h(x)=48-4x

7 0
3 years ago
41.3+0.7 adding and subtracting decimals
viktelen [127]
The answer would be 42
Because the 0.3 (from the number 41.3) and 0.7 make 1 so basically it would be 41+1=42
(Sorry if wrong! Mark brainiest if right!)
8 0
2 years ago
Read 2 more answers
What is the value of p if the line that passes through (2,-4) and (p,8) has a slope of 1/2? ​
Irina18 [472]

Answer:

Step-by-step explanation:

(2,-4)....x1= 2 and y1 = -4

(p,8).....x2 = p and y2 = 8

slope(m) = 1/2

now use the slope formula (y2 - y1) / (x2 - x1) and sub in what we know...

slope(m) = (y2 - y1) / (x2- x1)

1 / 2 = (8 - (-4) / (p - 2)

1 / 2 = (8 + 4) / (p - 2)

1/2 = 12 / (p - 2) .....now multiply both sides by (p - 2)

1/2(p - 2) = 12

1/2p - 1 = 12

1/2p = 12 + 1

1/2p = 13

p = 13 / (1/2)

p = 13 * 2/1

p = 26

so the value of p is 26

6 0
3 years ago
How to do this question plz answer me step by step plzz plz ​
Iteru [2.4K]

Answer:

£13496.80

Step-by-step explanation:

We can ignore the £ sign for now, that is just units.

If we decrease a number by 4.5%, we will have to find 100-4.5=95.5% of 14132.77.

We can easily do this by setting up a proportion.

\frac{x}{14132.77} = \frac{95.5}{100}

Multiply 14132.77 by 95.5:

14132.77\cdot95.5=1349679.535

Divide by 100:

1349679.535\div100=13496.79535

Rounding this to two decimal places, it simplifies to 13496.80.

Hope this helped!

4 0
3 years ago
To make fruit punch, Mrs.Casey adds 1,200 milliliters of water to 850 milliliters of syrup. How many liters of fruit punch does
konstantin123 [22]
1200 + 850 = 2050 ml

convert ML into L which makes it become 2.05 L

so your answer is 2.05L of fruit juice is made
3 0
3 years ago
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