Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
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
#SPJ1
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
