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
GrogVix [38]
3 years ago
7

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

Mathematics
1 answer:
nikitadnepr [17]3 years ago
6 0

Answer:

\sum_{n=0}^9cos(\frac{\pi n}{2})=1

\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0

\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}

Step-by-step explanation:

\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))

=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})

=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1

2nd

\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}

=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0

3th

\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))

=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}

What we use?

We use that

e^{i\pi n}=cos(\pi n)+i sin(\pi n)

and

\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}

You might be interested in
Carl’s square swimming pool has a volume of 1000 cubed feet. What are dimensions of his pool?
RUDIKE [14]

Answer: the answer is down bellow

Step-by-step explanation:

x3-10oo Dimensions ft each S.

5 0
3 years ago
50 points
mixas84 [53]
I believe it’s b I am not sure
Step by step explanation
8 0
3 years ago
Read 2 more answers
If 12% of x is equal to 6% of y, then 18% of x will be equal to how much percent of y ?​
Lelu [443]

Answer:

y=9%

Step-by-step explanation:

x=18%

y=9%

It is in a pattern like x=y+y

7 0
3 years ago
Read 2 more answers
Reed bought 1.8 pounds of green beans. The green beans cost $1.27 per pound. What was the total cost of Reed’s green beans? Roun
STALIN [3.7K]

Answer:

2.3

Step-by-step explanation:

5 0
3 years ago
Bryan is baking cookies for Zachary's birthday party. Bryan uses 1 cups
Nikolay [14]

Answer:

1 more cup

Step-by-step explanation:

1:10

x:50

10*5=50

1*5=5

5-4=1

1 more cup

8 0
3 years ago
Other questions:
  • This is a review for my exam but I need it now please!
    11·1 answer
  • How can I convert 35/21 two mixed numbers written in simplest form!Help Me please
    11·1 answer
  • A 26' long painting is how many inches long?
    13·1 answer
  • Why should you look out for a pig that knows karate?
    12·2 answers
  • A restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni. Of these, 2/3 also have pepp
    14·2 answers
  • Please help with this simple question!!!
    8·1 answer
  • Pls look at the picture !!
    8·1 answer
  • Which statement is true regarding the line y=−4x+13?
    6·1 answer
  • For brainiest:):):)):):):):):):):)
    15·1 answer
  • Ismail tried to prove that sin(θ) = cos(90°− θ) using the following diagram. His proof is not correct.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!