Alpha writes the infinite arithmetic sequence\(\[10, 8, 6, 4, 2, 0 ,\ldots.\]\)
Beta writes the infinite geometric sequence\(\[9, 6, 4, \frac{8}{3}, \frac{16}{9}, \ldots.\]\)
Gamma makes a sequence whose term is the product of the term of Alpha's sequence and the term of Beta's sequence:\(\[10\cdot 9 \quad,\quad 8\cdot 6\quad ,\quad 6\cdot 4\quad,\quad 4\cdot \frac83\quad,\quad 2\cdot \frac{16}{9}\quad,\quad \ldots.\]\)
What is the sum of Gamma's entire sequence?
