Mathematics College

Calculus hw, need help asap with steps.

Answers

Answer 1

Answers are in bold

S1 = 1

S2 = 0.5

S3 = 0.6667

S4 = 0.625

S5 = 0.6333

=========================================================

Explanation:

Let [tex]f(n) = \frac{(-1)^{n+1}}{n!}[/tex]

The summation given to us represents the following

[tex]\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\[/tex]

There are infinitely many terms to be added.

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The partial sums only care about adding a finite amount of terms.

The partial sum [tex]S_1[/tex] is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say [tex]S_1 = f(1) = 1[/tex]

I'm skipping the steps to compute f(1) since you already have done so.

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The second partial sum is when things get a bit more interesting.

We add the first two terms.

[tex]S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\[/tex]

The scratch work for computing f(2) is shown in the diagram below.

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We do the same type of steps for the third partial sum.

[tex]S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\[/tex]

The scratch work for computing f(3) is shown in the diagram below.

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Now add the first four terms to get the fourth partial sum.

[tex]S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\[/tex]

As before, the scratch work for f(4) is shown below.

I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.

This means something like [tex]S_3 = S_2 + f(3)[/tex] and [tex]S_4 = S_3 + f(4)[/tex]

In general, [tex]S_{n+1} = S_{n} + f(n+1)[/tex] so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.

-------------------

Let's use that recursive trick to find [tex]S_5[/tex]

[tex]S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333[/tex]

The scratch work for f(5) is shown below.

Related Questions

How do you convert 3 1/3 yards to inches? Use the drop-down menus to explain your answer.

Answers

Since, there are 36 inches in 1 yard, multiply 3 1/3 by 36

So, 3 1/3 yards = 120 inches

Answer:

120 inches

Step-by-step explanation:

To convert 3 1/3 yards to inches, you first need to figure out how many inches are in one yard. 1 yard=36 inches.

After this, you would turn your mixed fraction into an improper fraction and then multiply by 36 inches. It would look like this:

10/3 * 36/1

Here, you would cancel out the common factors by factoring 36 by 3.

12*3=36 ----> 10/3 * [tex]\frac{3(12)}{1}[/tex] ----->

Lastly, multiply 10 by 12 and your answer would be 120 inches.

.325 equals what fraction

Answers

Answer:

according to desmos scientific calculator, the answer is 13/40

13/40 is the correct answer

Wesley can use the equation y=3x to calculate how far he has walked, where y represents the number of miles walked, and x represents the number of hours walked. How many hours must Wesley walk to travel 16.5 miles?

Answers

16.5/3 = 5.5

Step-by-step explanation:

becuase he needs to walk 16.5 miles. and he can walk 3 miles per x(hour)

you need to devide distance by speed to get time.

Need answer ASAP will give BRAINLEST

Please put a full answer thank you

Answers

Answer:
1. It means they saved $125 in 10 months
2. y = 25/2

heresa earned scores of 88 points, 84 points, 88 points, and 91 points on four tests. What is the lowest score she can get on the fifth test and still finish with an average score of 90 points?

96 points
97 points
98 points
99 points

Answers

Answer:

99 points

Step-by-step explanation:

total of scores of 4 tests = 88 + 84 + 88 + 91 = 351

5 tests with an average score of 90:

⇒ total of scores = 5 × 90 = 450

Lowest score of 5th test = 450 - 351 = 99 points

Answer:

99 points

points scored:

88 points , 84 points, 88 points , 91 points, let the fifth test points be "n"

given score with an average 90 points

[tex]\sf \rightarrow \dfrac{88 +84+88+91+n}{5} =90[/tex]

[tex]\sf \rightarrow 351+n =90 (5)[/tex]

[tex]\sf \rightarrow n =450-351[/tex]

[tex]\rightarrow \sf n = 99[/tex]

Answer:

3.
Find c when a = -4 and b = 2
a-7
C=-
b

Answers

Answer:

[tex]c = 15[/tex]

Step-by-step explanation:

[tex]b = 2a - 7[/tex]

[tex]b = 2(-4) -7[/tex]

[tex]b = (-8)-7[/tex]

[tex]b = (-15)[/tex]

[tex]c = -(-15)[/tex]

[tex]c = 15[/tex]

Round each amount to the nearest hundred to find an estimate of:

3891 ÷ 289

Answers

Answer:

Step-by-step explanation:

Estimates are often made by rounding the operands to 1 or 2 significant digits. Here, that is accomplished by rounding each number to the nearest hundred.

Rounded to hundreds, the problem becomes ...

3900 ÷ 300

= 39/3 = 13

An estimate of the quotient is 13.

Answer the question 3523+4353

Answers

Answer:

7,876

Step-by-step explanation:

brainliest please

PLEASE EXPLAIN’

Which set of numbers correctly
shows a number, its opposite, and
its absolute value, in that order?
A 98.4
-98.4 98.4
B -74.3 -74.3
-74.3 74.3
C 46.2 46.2 -46.2
D 28.9 -28.9 -28.9

Answers

Answer:

Step-by-step explanation:

because -98.4 is the opposite of 98.4 and 98.4 is it's absolute value

(4a^2/3 b^1/2)(2a^1/3 b^3/2)

Answers

Answer:

8ab^2

Step-by-step explanation:

(4a^2/3 x 2a^1/3)(b^1/2 x b^3/2)

8a^(2/3+1/3) x b^(1/2+3/2) = 8a^1 x b^2

How do I get the answer??

Answers

Answer:

4√10

Step-by-step explanation:

Hello!

Let's first simplify the radical.

We can do this by expanding the radical:

We need to pull out a perfect square factor to expand a radical and simplify it. In 45, we have 9 and 5 multiplied, and 9 is a perfect square.

Let's work with √45:

√45 can be written as √9 * √5 (using the rule √ab = √a * √b)√9 simplifies to 3, so it is 3√5

Now we can simplify the operation in the parenthesis by combining like terms:

3√5 + √5√5 + √5 + √5 + √54√5

Now using the same rule as above, we can multiply the values:

√2(4√5)4√10

Your solution is 4√10

sin^2(theta)(1+cot^2(theta))-1=0

Answers

Hope it helpssss….best of luck

Find the question. 1/3 +(5/7)=

Answers

Answer:

22/21

Step-by-step explanation:

1/3 + 5/7

LCM of 3,7 = 3 x 7 = 21

1/3

= 1/3 x 7/7

= ( 1 x 7 )/( 3 x 7 )

= 7/21

5/7

= 5/7 x 3/3

= ( 5 x 3 )/( 7 x 3 )

= 15/21

1/3 + 5/7

= 7/21 + 15/21

= ( 7 + 15 )/21

= 22/21

how many times should you expect to see heads if a fair coin is tossed 3500 times?

Answers

Answer:

1750

Step-by-step explanation:

If you flip a coin, you should theoretically get heads 50% of the time and tails 50% of the time. So in this case you would get heads 1,750 times.

based on sample 2, how many students from the entire student population would prefer not to start at 7:45 am

Answers

Answer:

270

Step-by-step explanation:

from web

Leo is testing different types of greenhouse material to determine which type is most effective for growing strawberry bushes. He purchases two different brands of tarps from a local store. Leo applies brand A to an area of the yard that receives full sunlight and brand B to another area of the yard that is in partial shade. He waters both areas daily. At the end of the study, Leo concludes brand A is more effective in growing strawberry bushes. Is Leo's conclusion valid? please explain how and why so I can understand

Answers

For Leo conclusion to be valid, he should apply both brand A and B to area receiving same amount of sunlight.

What is bias?

Bias is an error due to sampling or testing by selecting or preferring one outcome over others.

Leo applies brand A to an area of the yard that receives full sunlight and brand B to another area of the yard that is in partial shade. This shows that Leo is bias.

For Leo conclusion to be valid, he should apply both brand A and B to area receiving same amount of sunlight.

Find out more on bias at: https://brainly.com/question/24491228

Answer:

His conclusion is not valid.

He should have put both tarps over the area of the yard that receives full sunlight. So that the experiment can be valid.

Step-by-step explanation:

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