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
Anni [7]
3 years ago
6

Show that the series is convergent by the alternating series test, and find the number of terms necessary to estimate the sum of

the series with an error of less than 0.05.

Mathematics
1 answer:
Murljashka [212]3 years ago
7 0

Answer:

6 terms

Step-by-step explanation:

2 − 2/4 + 2/9 − 2/16 + ...

∑ (-1)ⁿ⁺¹ 2 / n²

Applying alternating series test:

lim(n→∞) 2/n² = 0

2/(n+1)² < 2/n², so the series is decreasing.

Therefore, the series converges.

2/(n+1)² < 0.05

(n+1)²/2 > 20

(n+1)² > 40

n+1 > 6.32

n > 5.32

n = 6

You might be interested in
Bruh- can someone pls help me out kindly I will give 13 points
ycow [4]

Answer:

\huge\boxed{\texttt{Yes. Explanation for why.}}

Step-by-step explanation:

If we have the equation y = \frac{1}{2}x - 4 and we want to test if the point (4,–2) satisfies the equation, we can plug the x and y values into the equation and see if they make the equation true.

4 is the x value, -2 is the y.

-2 = (\frac{1}{2}\cdot4)-4

-2 = 2 - 4

-2 = -2

So this does satisfy the equation.

Hope this helped!

7 0
3 years ago
Read 2 more answers
PLEASE HELP ME IN MATH ITS URGENT
Alika [10]

Answer:

D

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the value of x?<br><br> Enter your answer in the box.<br> units
snow_tiger [21]

9514 1404 393

Answer:

  x = 25

Step-by-step explanation:

The parallel lines divide the triangle sides proportionally.

  x/40 = 15/24

  x = 40(15/24) . . . . multiply by 40

  x = 25

5 0
3 years ago
Hippalectryon
horrorfan [7]
Since the stadium is 6 mi from the practice field which is itself 1 mi from the house, it can either be (1+6)=7 mi North or (1-6)=-5 -> 5 mi South depending on the North/South direction.

the answer is thus A
7 0
3 years ago
David bought a poster for an art project. The poster is 2.7 ft wide and 3.9 ft tall. What is the area of the poster? Enter your
algol13
10.53 ft is the Area. :D:D
7 0
3 years ago
Other questions:
  • Is 15/4 an irrational number?
    14·1 answer
  • 21 students went on an exchange program to hong kong. There were 11 more women than men. How many woman are there?
    15·1 answer
  • It's on there plzz help
    5·1 answer
  • Which objects may have a mass greater than 300 grams
    14·1 answer
  • PLZ HELP A GIRL OUT ASAP !!!
    15·2 answers
  • In the diagram, △NPQ ∼ △NLM and PL = 8.
    6·1 answer
  • How many squares can you count?<br><br> A) 5<br> B) 4<br> C) 8<br> D) 6
    8·2 answers
  • Some friends are going to play laser tag. The cost of one game is $7.50. Each friend also purchase a drink for $3.50. Write an e
    7·1 answer
  • Simplify the following polynomial expression.
    13·1 answer
  • Please help me graph
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!