Respuesta :
Determine whether each infinite geometric series diverges or converges. The series converges.
If the series converges, state the sum. 1+ 1/4 + 1/16 + . . . .
The sum of the infinite series is 4/3
What is the sum of the infinite series?
Given:
[tex]a(\text{ the first term })=1\\\\r=\frac{a_{2} }{a_{1} } =\frac{1/4}{1} =\frac{1}{4}\\[/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{1}{1-\frac{1}{4}}=\frac{4}{3}[/tex]
The sum of the infinite series is 4/3
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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