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
sammi is trying to wrap a gift for her brother. the gift fits into a cube-shaped box with a side length of 9 inches. how many sq
Flauer [41]

Answer:

A=486\ \text{inches}^2

Step-by-step explanation:

The area of a cube shaped box is given by :

A=6s^2

Where

s is the side length and A is the surface area

We have, s = 9 inches

So,

A=6\times (9)^2\\\\A=486\ \text{inches}^2

So, the required area is 486\ \text{inches}^2.

8 0
2 years ago
Find the area of the shaded region.
miv72 [106K]

Answer:

The answer would be 27π

Step-by-step explanation:

the area is 36pi and the shaded region is 3/4 of the circle, as a 90 degree angle is 1/4 of a 360 degree circle. 3/4 of 36pi is 27pi

8 0
2 years ago
Read 2 more answers
What information does the point-slope form of a linear equation reveal about a line?
Rudik [331]
It reveals the slope and a single point on the line
3 0
3 years ago
Help with finding g(f(x))<br> f(x) = x squared - 3x + 2 <br> g(x)= x+2
n200080 [17]

Answer:

=x+2

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
I’m so bad at this ughhhhhhhhhhhhhhhhhhh
Alexus [3.1K]

Answer:

a)6

b)v^2-u^2/2a

Step-by-step explanation:

a)Given that,

u=12

a= -6

s=9

We know that,

v^2=u^2+2as

or, v^2=(12)^2+2×(-6)×9

or,v^2=144-108

or,v^2=36

or, v=√36

∴v=6

         (Ans)

b)If ,v^2=u^2+2as

then, u^2+2as=v^2

or,2as=v^2-u^2

or, s=v^2-u^2/2a

∴s=v^2-u^2/2a

Hope ya find it helpful.. Thanks a lot...

6 0
3 years ago
Other questions:
  • Geometry question, please help me
    6·1 answer
  • I need help can someone pls find the answer
    15·1 answer
  • JK Rowling is autographing some of the new Harry Potter books. A store sells 56 books and she is able to autograph 5/8 of the bo
    12·1 answer
  • PLLLLZ I WILL GIVE BRAINIEST ANSWER AND 72 PTS
    6·1 answer
  • Tory and Emilio's motorboats travel at the same speed Tory pilots her boat 60 km before docking Emilio continues for another 4 h
    15·1 answer
  • PLEASE HELP, question in image
    12·2 answers
  • What is 0/0
    11·2 answers
  • Why do systems of nonlinear equations sometimes have more than one solution​
    9·1 answer
  • PLS DO ALL thank you
    12·1 answer
  • Rewrite using exponential notation \root(6)((4\pi )^(3))
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!