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
Lyrx [107]
3 years ago
5

Which of the following series is/are convergent by the alternating series test?

Mathematics
1 answer:
sashaice [31]3 years ago
4 0

Answer:

I and II only

Step-by-step explanation:

According to the alternating series test:

For a series ∑(-1)ⁿ aₙ or ∑(-1)ⁿ⁺¹ aₙ

If lim(n→∞) aₙ = 0

and aₙ is decreasing,

then the series converges.

(I) aₙ = 1 / ln(n)

lim(n→∞) 1 / ln(n) = 0.

1 / ln(n) > 1 / ln(n+1).

This series converges.

(II) aₙ = n / (n²+1)

lim(n→∞) n / (n²+1) = 0.

n / (n²+1) > (n+1) / ((n+1)²+1) for n ≥ 1.

This series converges.

(III) aₙ = 2n / (5n−1)

lim(n→∞) 2n / (5n−1) = 2/5.

The alternating series test is inconclusive for this series.

You might be interested in
Shanice won 88 pieces of gum playing the bean bag toss at the county fair. That was 4 more than twice as many as Greg. How many
Kay [80]

Answer: 42 pieces of gum

Step-by-step explanation: 2x+4=88

4 0
3 years ago
Plz help ASAP it’s timed
Nuetrik [128]
I cant see the image but just wanted to lyk u should use the mathaway app it gives you answers and an explanation instantly
3 0
3 years ago
Lexia ran three laps around her neighborhood. Each lap is 1 and StartFraction 3 over 8 EndFraction miles. Which is the best esti
FrozenT [24]

Answer: The best estimate of the number of miles that Alexia run is 4 miles.

Step-by-step explanation:

Since we have given that

Length of lap is given by

Number of laps around her neighborhood = 3

So, Total number of miles that Alexia ran is given by

Hence, the best estimate of the number of miles that Alexia run is 4 miles

3 0
2 years ago
If nx10^p is a positive number written in scientific notation which statements must be true? Select all that apply
liq [111]

For this case we have the following number written in scientific notation:


n * 10 ^ p

We know that this number is greater than zero because it is a positive number.

Therefore, the following statements are true:

p ∈ (-∞, ∞)

n must be between 1 and 10

n ∈ [1, 10]

Answer:

The following statements are correct about the number written in scientific notation:

p ∈ (-∞, ∞)

n ∈ [1, 10]

3 0
3 years ago
At a book sale,your sister uses an equal number of quarters and nickels to buy a $1.20 book. How many quarters and how many nick
REY [17]

Answer:4 quarters and 4 nickels

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • 10°5 / 10*3*<br> I need help answering this question
    7·2 answers
  • Which could be the area of one face of the rectangular prism? Select three options.
    12·1 answer
  • O que é uma divisão finita?
    15·2 answers
  • Is it true that square roots can be compared and ordered by comparing and ordering the numbers underneath the radical symbol?
    6·1 answer
  • If QR is 7 less than twice X, RS is 61 less than 5 times x, and QS is 11 more than x, find X and the measure of each side.
    10·1 answer
  • The area of a circle will _____ be larger than the area of a polygon circumscribed about the circle.
    9·1 answer
  • 3× - 2y = 13, 2x +2y =0​
    7·1 answer
  • what is 1423443234423423235356536/234325464646546646465642131232132131=????????????????????????????????????????????????????
    7·1 answer
  • What is 29.1 + 78.9+ 41.5
    7·2 answers
  • What is a simpler form of the radical expression?<br><br> SOMEONE PLEASE HELP!!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!