The second option of the geometric series shows convergence in which r is less than 1.
What is the convergence of geometric series?
The convergence of the geometric series depends on the value of the common ratio that is r if r is less than 1 then only the geometric series would converge.
In the first option r is 4 which is more than 1 so, the series does not converge.
In the second option [tex]\sum 5(3/4)^{n-1}[/tex]
r is 3/4 which is less than 1 so, the series converges.
In the third option r is 7/5 which is more than 1 so, the series does not converge.
In the fourth option r is 1 which is equal to 1 so, the series does not converge.
Thus, the second option is correct.
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