1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Katena32 [7]
2 years ago
10

Calculus hw, need help asap with steps.

Mathematics
1 answer:
nikdorinn [45]2 years ago
7 0

Answers are in bold

S1 = 1

S2 = 0.5

S3 = 0.6667

S4 = 0.625

S5 = 0.6333

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

Explanation:

Let f(n) = \frac{(-1)^{n+1}}{n!}

The summation given to us represents the following

\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\\\\

There are infinitely many terms to be added.

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

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

The partial sum S_1 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 S_1 = f(1) = 1

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

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

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

We add the first two terms.

S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\

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

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

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

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\\\\\\

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

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

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

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\\\\\\

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 S_3 = S_2 + f(3) and S_4 = S_3 + f(4)

In general, S_{n+1} = S_{n} + f(n+1) 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 S_5

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

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

You might be interested in
What is the slope of the line that passes through the following points:<br> (4, -3), (-5, 10)
umka21 [38]

Answer:

-9/13

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

10-(-3)/-5-4

13/-9

-9/13

Best of Luck!

5 0
3 years ago
Helpppp a girl outtt i will give brainlest
Ivenika [448]

Answer:

Y= 40

Step-by-step explanation:

I know the y equals 40 because I used

a {}^{2}  + b {}^{2}  = c {}^{2}

But for z and x I got stuck, so I hope I helped you a little to move forward with this problem.

YOU CAN DO THIS!!!!!

7 0
3 years ago
The three inside angles (A,B and C) of a right-angled triangle are in the ratio 7:18:11. Th smallest angle is 35. Work out angle
lions [1.4K]

Answer:

<A = 35degrees

<B =90degrees

<C = 55degrees

Step-by-step explanation:

Given the ratios of a triangle as 7:18:11

Total ratio = 7+18+11

Total ratio = 36

Since the smallest angle is 35degrees, hence <A = 35degrees

Get angle B;

<B = 18/36 * 180 (sum of angle in a triangle is 180degrees)

<B = 1/2 * 180

<B = 90degrees

Get angle C;

<C = 11/36 * 180

<C = 11 * 5

<C = 55degrees

Hence the value of A, B and C are 35, 90 and 55 degrees repectively

3 0
3 years ago
(6.4×10^4)+(5.2×10^4)
Volgvan

6.4(104)+5.2(104)

=(6.4)(10000)+5.2(104)

=64000+5.2(104)

=64000+(5.2)(10000)

=64000+52000

=116000


7 0
3 years ago
Read 2 more answers
How many tens are in 192
posledela

19 tens are in 192 if you multiply 19 by 10 you will get 190 so the answer is 192 hope this helped brainly plz if correct

3 0
3 years ago
Read 2 more answers
Other questions:
  • Find the average of the data set: {12, 8, 4, 6, 10}<br><br> NEED HELP ASAP!!!!!!!
    9·2 answers
  • Maria added 45,273 and 37,687 and got the sum of 70,960. is maria's answer reasonable? explain.
    14·1 answer
  • What is -(5x+6)-x=-6-6x
    8·1 answer
  • The grades in period 3 Algebra 2 have an average of 82% and vary by 12 percentage points. Formulate an absolute value equation t
    7·1 answer
  • PLEASE HELP!!!!!! Answer fast!!! What is the value of n in the equation below?
    14·2 answers
  • Need as soon as possible
    11·1 answer
  • Samantha bought 26 total fish. Each goldfish cost $3 and each guppy costs $4. She spent $86 total. How many guppies did she buy?
    10·1 answer
  • on a lake, Carol rowed a boat for 1/8 mile. Then luke rowed the boat for 3/8 mile. how far did carol and like row in all? simpli
    9·1 answer
  • What is the volume of a sphere with a diameter of 7.9 ft
    5·1 answer
  • Given circle O lies perfectly within square ABCD. If side BC = 6.84, then what is the area of the orange region?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!