The series diverges because it does not have a sum option, fourth is correct.
What is the 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 get closer and closer to a certain number.
We have an infinite series:
[tex]\rm \sum ^{\infty}_{n=1}\dfrac{3}{4}(2)^n[/tex]
[tex]\rm \sum ^{\infty}_{n=1}3(2)^{n-2}[/tex]
The above series is geometric series with first term 2 and the common ratio is 2.
Here 2>1
By the ratio test, the series is divergent.
Since the common ratio is greater than 1 the sum will be infinite.
Thus, the series diverges because it does not have a sum option, fourth is correct.
Learn more about the convergent of a series here:
brainly.com/question/15415793
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