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
Mama L [17]
2 years ago
12

Use the Ratio Test to determine whether the series is convergent or divergent.

Mathematics
1 answer:
natka813 [3]2 years ago
3 0

Answer:

The series is absolutely convergent.

Step-by-step explanation:

By ratio test, we find the limit as n approaches infinity of

|[a_(n+1)]/a_n|

a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)

a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)

[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]

= |-3n³/2(n+1)³|

= 3n³/2(n+1)³

= (3/2)[1/(1 + 1/n)³]

Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity

= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity

= 3/2 × 1

= 3/2

The series is therefore, absolutely convergent, and the limit is 3/2

You might be interested in
(j-1)(-3) I need help solving the distributive property.
Reptile [31]

Answer:

Step-by-step explanation:

-3*j = -3j

(-3)(-1) = 3

Answer

-3j + 3 Notice the sign change. Be careful about that when signs are used with the distributive property.

5 0
3 years ago
Help I’ve been stuck on these questions
Svetach [21]

Answer:

3+4x

7-12

2x+14=18

four times a number

four times a number is added to seven

Step-by-step explanation:

6 0
2 years ago
Brainliest, what is the total measure of angles 8 and 5 of angle 7 equals 61
guapka [62]
Lines equal 180°. The line with angles 5 and 7 equals 180°. If angle 7 equals 61°, then angle 5 equals 119° (180° - 61°= 119°).

Angles 5 and 8 are opposite vertical angles, which are always congruent (equal), so angles 5 and 8 both equal 119°.

119° (angle 5) + 119° (angle 8)= 238°


ANSWER: The two angles total 238° (bottom choice).

Hope this helps! :)
7 0
3 years ago
Prove that the value of the expression<br> (16^3–8^3)(4^3 +2^3) is divisible by 63.
Darya [45]

Answer:

Step-by-step explanation:

16^3 - 8^3

Take out 8^3 as a common factor.

16^3 = 2^3 * 8^3

8^3(2^3 - 1)  

8^3(8 - 1) = 8^3 * 7

(4^3 + 2^3)     Expand

64 + 8            Combine

72

72 = 9 * 8

Conclusion

(8*3 * 7 )(9*8)

7*9 = 63

So any number containing 63 will divide into the reduced form of

(16^3–8^3)(4^3 +2^3)

7 0
2 years ago
4x - 6 = 2x - 2 does anyone know the answer to dis
mel-nik [20]

4x-6=2x-2

You then would eliminate 6, by adding 6 to both sides

4x=2x+4

Then you want all of the X's on the same side, so you subtract 2x from both sides.

2x=4

Then to isolate the X, you divide by 2

2=x

The answer is x=2

4 0
3 years ago
Other questions:
  • By treating savings as an ___ it guarantees that you will save the money instead of spending it
    6·2 answers
  • please help.......if Frans fudge recipe calls for 2 1/2 cups of sugar and she increases it by 2/5 of a cup, how much sugar does
    7·1 answer
  • At 3:00 p.m., Jamie leaves her house and drives north to the beach. She arrives at 5:30 p.m. Also leaving at 3:00 p.m., her brot
    11·2 answers
  • 20 POINTS!
    6·1 answer
  • 7th grade math
    9·1 answer
  • Solve the equation for x. 10x= 120​
    8·2 answers
  • I need help which is it?
    9·1 answer
  • Solve using the Quadratic Formula.<br><br> 3x2 + 2x + 1 = 0
    15·1 answer
  • X/5 + 3=2<br>A) -5<br>B) 25<br>c)5 <br>D)-1/5​
    15·2 answers
  • FREE PLS HELP
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!