# Are the series absolutely, conditionally convergent, or divergent?

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.

## Related Questions

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.

brainly.com/question/14783619

#SPJ1

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%

D

Step-by-step explanation:

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

Step-by-step explanation:

Complete the following proof

Step-by-step explanation:

statment/reason

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 downward..so 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