Question # The sum of the series ( 1+frac{1}{4}+frac{1}{16}+frac{1}{64}+ldots ldots infty ) is

# The sum of the series ( 1+frac{1}{4}+frac{1}{16}+frac{1}{64}+ldots ldots infty ) is

(1)( frac{8}{7} )

(2) ( frac{6}{5} )

(3) ( frac{5}{4} )

(4) ( frac{4}{3} )

Solution

( 1+1/_{u}+1/_{16}+1/_{6 4}+cdots cdot cdot e )

above series in ( G cdot p )

( a_{1}=1 quad, quad x_{1}=1 / 4 quad b / a=1 / u times 1=1 / 4 )

( S_{x}=frac{a_{1}}{-r_{1}+1} )

( S_{0}=frac{1}{1-y_{4}}=frac{4}{3} )