ttmarkstt
contestada

WILL GIVE BRAINLIEST AND FIVE STARS TO CORRECT ANSWER


Determine whether the sequence converges or diverges. If it converges, give the limit.

108, -54, 27, negative 27 divided by 2, ...

Answer choices:
A) Converges; 216
B) Diverges
C) Converges; 540
D) Converges; 0

Respuesta :

sqdancefan

Each successive term has a magnitude that is half that of the term before. The general term is 108·(-1/2)^(n-1). This will be arbitrarily small as n gets larger. The sequence ...

... D) Converges to 0

_____

The sum of the sequence converges to 72.

Answer:

Option: D is the correct answer.

                       D) Converges; 0

Step-by-step explanation:

We are given a following sequence:

108,-54,27,-27/2,...

We have to determine whether the following sequence converges or diverges

As we can see that each term of the sequence is equal to the previous term divided by -2

i.e. [tex]a_{n+1}=\dfrac{a_{n}}{-2};\ a_{1}=108[/tex]

Now, the following sequence is convergent by the property that it's complementary pair of subsequences converge to the same limit and hence the sequence is convergent.

Here the odd set of subsequence i.e.

[tex]a_1,a_3,a_5,....[/tex]

converge to zero.

and also the even set of subsequence i.e.

[tex]a_2,a_4,a_6,...[/tex]

converge to zero.

Hence, the sequence converge to zero.

Otras preguntas