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

# Fine 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

The given series is an intinite gp in notich

[

begin{array}{l}

text { which } 9=1, gamma=frac{1}{4}

S_{infty}=frac{9}{(1-gamma)} quad( text { Sum }

end{array}

]

( left(begin{array}{c}text { Sum } 05 text { infinite term }end{array}right) )

[

=frac{1}{1-frac{1}{4}}

]

[

begin{array}{l}

=frac{frac{1}{4-1}}{4}

S_{infty}=frac{4}{3}

end{array}

]

option (4) is correct dear