Respuesta :
The sequence diverges because the value of the absolute common ratio r is greater than the 1.
What is convergent of a series?
A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.
We have series:
9, 27, 81, 243....
The above series is a geometric progression with common ratio r is 3
[tex]\rm r =\dfrac{27}{9}[/tex]
r = 3
We know the formula for a geometric sequence:
[tex]\rm S_n = 9(3)^n[/tex]
[tex]\rm S_n = 3^{n+2}[/tex]
A geometric series converges only if the absolute value of the common ratio:
r < 1 and
It diverges if the ratio ≥ 1
Here the value of r = 3 which is greater than the 1 so the sequence diverges.
Thus, the sequence diverges because the value of the absolute common ratio r is greater than the 1.
Learn more about the convergent of a series here:
brainly.com/question/15415793
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