Let \left(a_{n}\right) and \left(b_{n}\right) be the sequences of real numbers such that
(2+i)^{n}=a_{n}+b_{n} i
for all integers n \geq 0, where i=\sqrt{-1}. What is
\sum_{n=0}^{\infty} \dfrac{a_{n} b_{n}}{7^{n}} ?
Answer Choices
A. \dfrac{3}{8}
B. \dfrac{7}{16}
C. \dfrac{1}{2}
D. \dfrac{9}{16}
E. \dfrac{4}{7}