Respuesta :

Does the infinite series converge or diverge? The series converges.

If it converges, what is the sum?

a. 1/2 + 3/4 + 9/8 + . . . . .

The sum of the infinite series is -1

What is the sum of the infinite series?

Given:

[tex]a(\text{ the first term})=\frac{1}{2} \\\\r(\text{ thecommon ratio})=\frac{a_2}{a_1} =\frac{3}{2}[/tex]

Since ,[tex]\vert r\vert < 1[/tex], the  infinite series converges.  

The sum of infinite geometric series is:

[tex]S_\infty=\frac{a }{1-r} ; -1 < r < 1\\\\S_\infty=\frac{\frac{1}{2}}{1-\frac{3}{2}}=-1[/tex]

The sum of the infinite series is -1

What is an infinite geometric series?

  • The result of an endless geometric sequence is an infinite geometric series.
  • There would be no conclusion to this series.
  • The total of all finite geometric series can be determined.
  • However, if the common ratio of an infinite geometric series is bigger than one, the terms in the sequence will grow steadily larger, and adding the larger numbers together will not yield a solution.

To learn more about infinite geometric series, refer:

brainly.com/question/27350852

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