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
Lilit [14]
3 years ago
14

Determine whether the series is convergent or divergent. 1 2 3 4 1 8 3 16 1 32 3 64 convergent divergent Correct:

Mathematics
1 answer:
Vanyuwa [196]3 years ago
5 0

Answer:

This series diverges.

Step-by-step explanation:

In order for the series to converge, i.e. \lim_{n \to \infty} a_n =A it must hold that for any small \epsilon>0, there must exist n_0\in \mathbb{N} so that starting from that term of the series all of the following terms satisfy that  |a_n-A|n_0 .

It is obvious that this cannot hold in our case because we have three sub-series of this observed series. One of them is a constant series with a_n=1 , the other is constant with a_n=3 , and the third one has terms that are approaching infinity.

Really, we can write this series like this:

a_n=\begin{cases} 1 \ , \ n=4k+1, k\in \mathbb{N}_0\\ 2^{k}\ , \ n=2k, k\in \mathbb{N}_0\\3\ , \ n=4k+3, k\in \mathbb{N}_0\end{cases}

If we  denote the first series as b_n=1, we will have that \lim_{k \to \infty} b_k=1.

The second series is denoted as c_k=2^k and we have that \lim_{k \to \infty} c_k=+\infty.

The third sub-series d_k=3 is a constant series and it holds that \lim_{k \to \infty} d_k=3.

Since those limits of sub-series are different, we can never find such n_0\\ so that every next term of the entire series is close to one number.

To make an example, if we observe the first sub-series if follows that A must be equal to 1. But if we chose \epsilon =1, all those terms associated with the third sub-series will be out of this interval (A-1, A+1)=(0, 2).

Therefore, the observed series diverges.

You might be interested in
ANSWER PLEASE FINAL DUE IN 3 HOURS
inna [77]

Answer:

B

Step-by-step explanation:

First thing to do here is to calculate the z-score

Mathematically;

z-score = (x-mean)/SD

here, x = 130, mean = 120 and SD = 10

Substituting these values

z-score = (130-120)/10 = 10/10 = 1

So the probability we want to calculate is;

P(z ≥ 1) = 1 - P(z <1)

From standard score table, P(z <1) = 0.15866

P(z ≥ 1) = 1-0.15866 = 0.84134

6 0
3 years ago
1. Use the image of the circle to identify the length of the radius, diameter, and circumference. Leave all answers in terms of
Grace [21]

Answer:

Radius =  r = 7.5

Diameter = d = 15

Circumference = C = 15π

Step-by-step explanation:

We are given the image of a circle with a straight line passing through the center of the circle and touching its edges. Such a line is known as the diameter of the circle. From the image we can see the length of the diameter of the circle is d = 15 units.

Radius is define as half of the diameter. Since the diameter is 15 units, the radius of the given circle will be half of 15 which is r = 7.5 units.

Circumference of the circle = C = 2πr

Using the value of radius(r), we can write the circumference as:

C = 2π(7.5) = 15π

5 0
2 years ago
I need some help pls
Nimfa-mama [501]
Answer is A, basically using the Pythagorean theorem but in a slightly different way, should still get you the same answer.
4 0
2 years ago
The function f is defined by f(x) = a+b/x where a and b are constant .given that f (3) = 2 and f (7) = -2.
ivanzaharov [21]

Answer:

f(x) = a+b/x

We = 0

So that  f(x) = 3+7/x  = f(x) = 3+7/-2 = 5 also 3+7/-2+2 = 10/0 = -1

Step-by-step explanation:

3 0
2 years ago
Which equation represents a line which is parallel to the line 3y−2x=−24?
Blizzard [7]

Answer:

Any equation of the line with slope 2/3.

Parallel lines have identical slope.

Step-by-step explanation:

3y - 2x = - 24

3y = 2x - 24

y = 2/3x - 8

3 0
2 years ago
Other questions:
  • A line passes through the points (3,5) and (2,0) what is the slope of the line?
    7·1 answer
  • How to write an equation of a horizontal line through a point?
    5·1 answer
  • From a box containing 10 cards numbered 1 to 10, four cards are drawn together. The probability that their sum is even is 21 21
    13·1 answer
  • a tree house has a square floor with a total area of 50 ft square. to the nearest tenth, what is the length of one side?
    15·1 answer
  • -How can you solve compound inequalities in one variable?
    6·1 answer
  • I need help on my homework... plz
    7·1 answer
  • K + 22 = 29<br> Solve the equation.
    5·2 answers
  • What is the equation of the line that passes through the point (-4, -7) and has a<br> slope of 5/2 ?
    10·1 answer
  • What is the slope of the line of the equation y = x + 4?
    13·2 answers
  • 1 quart=4 cups (whats the answer?)
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!