Answer:
D.) Converges; 256
Step-by-step explanation:
x0= 192
x1 = 48 = 192/4
x2 = 12 = 192/(4 x 4)
Therefore, this series can be written as:
[tex]x_n = \frac{192}{4^n}[/tex]
Applying limits at infinity:
[tex]\lim_{n \to \infty} x_n= \lim_{n \to \infty} (\frac{192}{4^n}) = \frac{192}{\infty}=0[/tex]
Since the terms of the series tend to zero, we can affirm that the series converges.
The sum of an infinite converging series is:
[tex]S=\frac{x_0}{1-r} \\S=\frac{192}{1-\frac{1}{4} }\\S=256[/tex]
Thus, the answer is D.) Converges; 256
