Find the sum of the infinite geometric series. 1+14+116+164+...

To find:
The sum of infinite geometric series.
Given:
The geometric series is $1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+...$
Concept used:
The sum of infinite term of the geometric series is
$S_{\mathrm{\infty }}=\frac{a}{1-r}(r<1)$
Here, a is first term, r is common ratio( less than 1) and $S_{\mathrm{\infty }}$ is the sum of the infinite series.
Calculation:
The first term of the geometric series is 1.
The common ratio can be obtained by the ratio of second term by first term.
$\frac{\frac{1}{4}}{1}=\frac{1}{4}$
The common ratio $\frac{1}{4}$ is less than 1.
Substitute $\frac{1}{4}$ for r and 1 for a in equation
$S_{\mathrm{\infty }}=\frac{1}{1-\frac{1}{4}}$
$=\frac{1}{\frac{4-1}{4}}$
$=\frac{4}{3}$
Thus, the sum of infinite geometric series is $\frac{4}{3}$

Answer is given below (on video)