Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
[tex]S_n=\sum^{\infty}_{n=1}4(\dfrac{1}{4})^{n-1}[/tex]
We need to find the value of S₄.
So, it means sum of 4 terms.
Here it form a geometric series:
a = 4 = first term
r = [tex]\dfrac{1}{4}[/tex] = Common ratio
And sum of n terms whose ratio is less than 1 is given by
[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\S_4=\dfrac{4(1-\dfrac{1}{4}^{4})}{1-\dfrac{1}{4}}\\\\S_4=\dfrac{4(1-0.25^4)}{1-0.25}\\\\S_4=\dfrac{4(1-0.0039)}{0.75}\\\\S_4=5.3125\\\\S_4=5\dfrac{5}{16}[/tex]
Hence, Option 'C' is correct.
