Mathematics

Problem

For every integer

n\ge 1

, let

a_n=\dfrac{7}{4^{n}+2}

. Which of the following inequalities is true for all such

n

? a)

a_n>\dfrac{7}{4^{n}}

a_n>\dfrac{7}{4^{\,n-1}}

a_n<\dfrac{7}{4^{n}}

a_n>\dfrac{7}{5^{n}}