Let $'x'$ denotes the value of the product $(1+a+a^2+a^3+....\infty)(1+b+b^2+b^3+....\infty)$ where $'a'$ and $'b'$ are the roots of the quadratic equation $11x^2-4x-2=0$ and $'Y'$ denotes the numerical value of the infinite series $(log_b2)^0(log_b5^{4^0})+(log_b2)^1(log_b 5^{4^1})+(log_b2)^2(log_b5^{4^2})+(log_b2)^3(log_b5^{4^3})+.....\infty$ where $b=2000$ then the value of ($XY$) equals.