17. Company A and Company B, both had a market share of $A$ in 1996. According to market analysis and predictions, Company A's market share in the $n$-th year (1996 being the 1st year) is $a_{n}=\frac{A}{40}\left(n^{2}-n+40\right)$, and Company B's market share has increased year by year since 1996, following the pattern shown in Figure 5.
(1) Observe Figure 5 and derive the expression for Company B's market share in the $n$-th year;
(2) According to the market rules of the regions where the two companies are located, if one company's market share is less than 20% of the other company's market share, the former will be acquired by the latter. It has been calculated that no acquisition will occur before 2015. Will an acquisition occur in 2015? Explain your reasoning.
Figure 5
17. (1) Let the market share of Company B in the $n$-th year be $b_{n}$. From the analysis of Figure 5, we get
$$
b_{n}=A+\frac{A}{2}+\frac{A}{4}+\cdots+\frac{A}{2^{n-1}}=\left(2-\frac{1}{2^{n-1}}\right) A .
$$
(2) According to the problem, 2015 is the 20th year, then
$$
\begin{array}{l}
a_{20}=\frac{A}{40}\left(20^{2}-20+40\right)=\frac{21}{2} A>10 A, \\
b_{20}=\left(2-\frac{1}{2^{19}}\right) A<2 A .
\end{array}
$$

Therefore, $\frac{b_{20}}{a_{20}}<\frac{2 A}{10 A}=20 \%$, which means $b_{20}<a_{20} 20 \%$. It is evident that in 2015, Company B will be acquired by Company A.