Are the series absolutely, conditionally convergent, or divergent?
Are the series absolutely, conditionally convergent, or divergent? - 2


Answer 1

Step-by-step explanation:

∑ sin(nπ/4) / (n³ + 3n)

This is less than 1 / n⁴ for all n > 1.  1/n⁴ is a convergent p-series, so the lesser series also converges.  │aₙ│converges for the same reason, so this is absolutely convergent.

∑ (-1)ⁿ⁺¹ ln(n + 1) / (n + 1)

This is an alternating series.  bₙ is positive and decreasing, and lim(n→∞) bₙ = 0, so the series converges.  Now we need to check if│aₙ│converges.  Using comparison test, │aₙ│is greater than 1/n for all n ≥ 6.  1/n is a divergent p-series, so the greater series│aₙ│also diverges.  So this is conditionally convergent.

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Calculate had a net income of 5 million dollars in 2010, while a small competing company, Computate, had anet income of 2 millions dollars. The management of Calculate develops a business plan for future growththat projects an increase in net income of 0.5 million per year, while the management of Computatedevelops a plan aimed at increasing its net income kshy15% each year.a. Create standard mathematical model (table, graph, or equations) for the projected net income for thenext 10 years for both companies. Make sure that each model is accurate and labeled properly so that itrepresents the situationb. If both companies were able to meet their net income growth goals, which company would you chooseto invest in? Why?c. When, if ever, would your projections suggest that the two companies have the same net income? Howdid you find this? Will they ever have the same net income again?
What is the w 4w+3w=63
What is the opposite of —3.2
Help please it due today thank u
35 points plz helpEvaluate −4(14)6x for x=13.Enter your answer as a fraction in simplest form in the box.

One package of tile will cover 3 square feet.How many packages will shee need 8,13,15,39​HELP ASAP


Hey there! :)


13 packages.

Step-by-step explanation:

Begin by finding the total area of this composite figure. Separate the figure into separate rectangles. Use the formula A = l × w to calculate the area of each:

Smaller rectangle:

Subtract 7 from 9 to find the width:

9 -7 = 2. Therefore:

2 × 2 = 4 ft².

Larger rectangle:

7 × 5 = 35 ft².

Add up the two areas to find the area of the entire figure:

4 + 35 = 39 ft².

If each package of tile covers 3 ft², simply divide to find the package of tiles needed:

39 / 3 = 13 packages.


Step-by-step explanation:

Henderson opened a coffee shop. He insured his store against fire for $150,000. What’s his premium if the rate per $100 is $0.79


Henderson premium for his coffee shop is $1185

Given in the question:

Henderson opened a coffee shop. He insured his store against fire for $150,000.

and, the rate of his premium per $100 is $0.79.

Now, According to the question:

Divide the value of the coffee shop by $100

= $150,000 / $100 = $1500

Multiply the quotient by the rate per $100

=    $1500 x  $.79 = $1185.

Hence, Henderson premium for his coffee shop is $1185.

Learn more about Premium Rate at:


The Williams are buying a house that costs $323,000 and can afford a 10% down payment. If the Williams want the lowest monthly payment, which loan option would you recommend?a. 15 year fixed, 5% down at a fixed rate of 5.5%
b. 30 year FHA, 3.5% down at a fixed rate of 6.25%
30 year fixed, 20% down at a fixed rate of 5.75%
d. 30 year fixed, 10% down at a fixed rate of 6%




Step-by-step explanation:

30 year fixed, 10% down at a fixed rate of 6%


Step-by-step explanation:

top answer is correct

Complete the following proof



Step-by-step explanation:


1) HK≅JK / given (S)

2) IK bisects ∠HKJ / given

3) ∠3≅∠4 / angle bisectors form congruent angles (A)

4) HK≅JK / given

5) IK ≅IK / reflexive propriety (S)

6) ΔIHK≅ΔIJK / SAS theorem of congruency

7) ∠1≅∠2 / corsponding parts of congruent Δs are ≅

8) IK bisects ∠HIJ / angle bisectors form congruent angles

If the absolute value of the correlation is approximately one, then the points lie close to a line that slopes upward or downward?



if it is positive then it goes upward and if negative it goes if it is approximately 1 then it will be constant or straight...

What number Could be added in the expression -4 -9 that the value of the expression is 0




Step-by-step explanation:

-4-9 gives -13

when +13 is added to -13 , the expression becomes +13+(-13) =13-13=0

if i’m understanding this correctly -9 + -4 is equal to -13 so wouldn’t you just add 13 to make it 0?

sorry if this is confusing
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