The sum of the first $n$ terms in the infinite geometric sequence $\left\{\frac{1}{4},\frac{1}{8},\frac{1}{16},\dots \right\}$ is $\frac{63}{128}$. Find $n$.
The value of n is 5.
There are 6 terms adding up to 63 / 128 as follows:
1 / 4 , 1 / 8 , 1 / 16 , 1 / 32 , 1 / 64 , 1 / 128 , >>Number of terms = 6>>Total Sum == 63 / 128
