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]
2 years ago
5

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

Mathematics
1 answer:
sashaice [31]2 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
Sean's house is currently worth $188,900. According to a realtor, house prices in Sean's neighborhood will increase by 4.8% ever
mrs_skeptik [129]

Answer  

Given

Sean's house is currently worth $188,900.

According to a realtor, house prices in Sean's neighborhood will increase by 4.8% every year.

To prove

Formula

Compound\quaterly\ interest = Principle (1 + \frac{r}{4})^{4t}

Where r is the rate in the decimal form.

As given

Take\ Principle\ = P_{0}

Rate = \frac{4.8}{100}

              = 0.048

Put in the formula

Compound\quaterly\ interest = P_{0}(1 + \frac{0.048}{4})^{4t}

Compound\quaterly\ interest = P_{0} (1 + \frac{0.048}{4})^{4t}

Compound\quaterly\ interest = P_{0} (1 + 0.012)^{4t}       Compound\quaterly\ interest = P_{0} (1.012)^{4t}  

Now also calculated monthly.

Formula

Compound\ monthly = Principle (1 + \frac{r}{12})^{12t}

As given

Take\ Principle\ = P_{0}

Rate = \frac{4.8}{100}

              = 0.048

Put in the formula

Compound\ monthly = P_{0} (1 + \frac{0.048}{12})^{12t}

Compound\ monthly = P_{0} (1 + 0.004)^{12t}

Compound\ monthly = P_{0} (1.004)^{12t}

As the approximation quarterly growth rate of the value of sean's house is near the Compounded quarterly interest .

Thus Option (A) is correct.

i.e

The expression (1.0118)^{4t} reveals the approximate quarterly growth rate of the value of Sean's house.




                                               

                                                       




6 0
3 years ago
Read 2 more answers
What is the slope of the line that goes through the points (1,-5) and (4,1)?
Anna007 [38]

Answer:

D. 2

Step-by-step explanation:

(1 - -5)/(4 - 1) = 6/3 = 2

3 0
3 years ago
Read 2 more answers
In a particular month, Ezhil spent one-fifth of her salary on shopping. Two-fifth of the remaining she gave to her sister. If sh
Oxana [17]

Answer:

Salary = Rs23000

Step-by-step explanation:

Given

Shopping = \frac{1}{5}

Sister = \frac{2}{5}R

Left over = Rs11,040

Required

Her salary in that month

Given that she spent \frac{1}{5} of her salary on shopping, this implies that she has \frac{4}{5} of her salary left

From what's left, she gave her sister \frac{2}{5}

This means she gave her sister \frac{2}{5} * \frac{4}{5}

Sister = \frac{8}{25}

Calculating a fraction of what's left

Left over = 1 -Shopping - Sister

Left over = 1  - \frac{1}{5}- \frac{8}{25}

Left over = \frac{25 - 5 - 8}{25}

Left over = \frac{12}{25}

Recall that she has Rs11,040

This means that

\frac{12}{25} of Salary = Rs11,040

Multiply both sides by \frac{25}{12}

\frac{12}{25} * \frac{25}{12} * Salary = Rs11,040 * \frac{25}{12}

Salary = Rs11,040 * \frac{25}{12}

Salary = \frac{Rs276000}{12}

Salary = Rs23000

Hence, her salary for that month was Rs23000

5 0
2 years ago
Read 2 more answers
Help in dying please​
Mkey [24]

Answer:

hello! :) i hope your having a wonderful day :)

Step-by-step explanation:

7 0
2 years ago
Write the following in algabraic expression: the sum of the number a and three times the square of the number b
ycow [4]

Answer:

a+3b^2

Step-by-step explanation:

6 0
1 year ago
Read 2 more answers
Other questions:
  • Leah likes the number 400 but not 500. She likes 900 but not 999.
    13·1 answer
  • Paula a college student earned $3,600 one summer during the following semester she spent $2500 for tuition $650 for rent and $43
    8·1 answer
  • What is the approximate average rate of
    5·1 answer
  • Can someone explain how they get the answer.
    10·2 answers
  • 2 times 4 squared................
    8·2 answers
  • -3*6<br> Multiplying and dividing integers
    15·1 answer
  • Help !! Is the work shown in the simplification below correct? Explain.
    11·2 answers
  • HELP ME PLS :(
    6·2 answers
  • The sales totals at Macy's food store have increased exponentially over the months. Which of these best shows the sales in the f
    9·1 answer
  • 85
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!