Answer :
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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