Respuesta :
Answer:
Diverges
There is no sum.
Step-by-step explanation:
A geometric series has a general formula of:
[tex]\sum ar^n[/tex]
Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges, but if |r| > 1, than the series diverges.
In this problem, the initial term is a = 36, the ratio can be found by:
[tex]r = \frac{39.6}{36}=\frac{43.56}{39.6}\\ r=1.1[/tex]
Since the ratio is r =1.1 and 1.1 > 1.0, the series diverges.
In a diverging series, it is not possible to determine the sum of infinite terms, since it would be infinite.
The geometric series diverges and the sum does not exists.
What is a Geometric Series ?
A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .
A geometric series has a general formula of:
∑arⁿ
Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.
In this particular case, the initial term is a=36 and each term is multiplied by 1.1 to get the next term
Therefore r = 1.1 and as it is >1 therefore the series diverges.
The sum of a divergent series is not finite so the sum does not exists.
To know more about Geometric Series
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