The sum represents an infinite geometric sequence, and it's result is given by: [tex]\frac{3}{16}[/tex].
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of an infinite sequence in which |q| < 1 is given by:
[tex]S = \frac{a_1}{1 - q}[/tex]
In this problem, we have that the first term and the common ratio are given, respectively, by:
[tex]a_1 = \frac{1}{4}, q = -\frac{1}{3}[/tex]
Hence:
[tex]S = \frac{\frac{1}{4}}{1 + \frac{1}{3}} = \frac{\frac{1}{4}}{\frac{4}{3}} = \frac{3}{16}[/tex]
More can be learned about geometric sequences at https://brainly.com/question/11847927
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