Answer:
The correct option is B
Step-by-step explanation:
\(\text{First term, }a_1 = 48\\\\\text{Common Ratio,r = }\frac{1}{4}\\\\\text{The sum of the geometric progression is given by :}\\\\Sum = \frac{a_1}{(1-r)}\\\\\implies Sum=\frac{48}{(1-\frac{1}{4})}\\\\\implies Sum = 48\times \frac{4}{3}=64\)
And the sigma notation for the above sum can be written as :
\(\sum_{i=1}^{\infty}a_1\cdot(r)^{i-1}\\\\\implies Sum = \sum_{i=1}^{\infty}48\cdot(\frac{1}{4})^{i-1}\)
Therefore, The correct option is B
