\[ \sum_{r=0}^{2 \pi} a_{r}(x-100)^{r}=\sum_{r=0}^{2 n} b_{r}(x-101)^{r} \text { and } a_{k}=\fr...
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\sum_{r=0}^{2 \pi} a_{r}(x-100)^{r}=\sum_{r=0}^{2 n} b_{r}(x-101)^{r} \text { and } a_{k}=\frac{2^{k}}{{ }^{k} C_{n}} \text { for all }
\]
\( kn_{1} \) then \( b_{n} \) equals
(A) \( 2^{n}\left(2^{n+2}-1\right) \)
(B) \( 2^{n}\left(2^{\Downarrow}+1\right) \)
(C) \( 2^{\prime \prime}\left(2^{n}-1\right) \)
(D) \( 2^{n+1}\left(2^{n}-1\right) \)
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