Question

What is the value of $1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+\frac{1}{256}+....?$

• A.
  $2$
• B.
  $\frac{7}{4}$
• C.
  $\frac{3}{2}$
• D.
  $\frac{4}{3}$

Answer 1

The correct option is D

$\frac{4}{3}$
This is a infinite Geometric Progression with first term (a) =1

$andcommonratio\left(r\right)=\frac{1}{4}$

The formula for finding the sum of infinite G.P is given by

$\frac{a}{1-r}$

$\frac{1}{1-\frac{1}{4}}=\frac{1}{3/4}=\frac{4}{3}$