The expression that defines Sn is option (A), Sn = lim n->∞ (1/4)^n is the correct answer.
What is a series?
A sequence is defined as an arrangement of numbers in a particular order. A series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers.
For the given situation,
The series is 1/4 + 1/16 + 1/64 + 1/256.
⇒ [tex]\frac{1}{4}+\frac{1}{16} +\frac{1}{64} +\frac{1}{256}[/tex]
⇒ [tex]\frac{1}{4}+\frac{1}{4^{2} } +\frac{1}{4^{3} } +\frac{1}{4^{4} }[/tex]
Thus the sum of this series can be obtained by the expression,
[tex]S_{n}= \lim_{n \to \infty} (\frac{1}{4^{n}})[/tex]
⇒ [tex]S_{n}= \lim_{n \to \infty} (\frac{1}{4})^{n}[/tex]
Hence we can conclude that the expression that defines Sn is option (A), Sn = lim n->∞ (1/4)^n is the correct answer.
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