The series 6 + 2 + 2/3 +..... is convergent and it converges to 9
The sequence is given as:
6 + 2 + 2/3 + ....
The above sequence has the following parameters
First term, a = 6
Common ratio, r = 1/3
As a general rule:
If the common ratio of a geometric series is between -1 and +1, then the series is convergent.
Otherwise, it is divergent
The above means that the series is convergent
This is so because the common ratio is inside the range -1 to +1
The convergent point is calculated as:
S = a/1 -r
So, we have
S = 6/1 - 1/3
Evaluate the difference
S = 6/(2/3)
Divide
S = 9
Hence, the series 6 + 2 + 2/3 +..... is convergent and it converges to 9
Read more about geometric sequence at
brainly.com/question/1509142
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