Answer:
The sum of the given geometric series and its sigma notation is given below :
Step-by-step explanation:
First term, a = 48
[tex]\text{Common ratio, r = }\frac{1}{4}[/tex]
The series is given to be geometric series and the sum of geometric series is given by :
[tex]S_n=\frac{a}{1-r}\\\\\implies S_n=\frac{48}{1-\frac{1}{4}}\\\\\implies S_n = 64[/tex]
And for sigma notation,
[tex]Sum = \sum_{i=1}^{\infty}a\cdot(r)^i-1\\\\\implies Sum = \sum_{i=1}^{\infty} 48\cdot(\frac{1}{4})^{i-1}[/tex]
