\( \sum_{r=0}^{2 n} a_{r}(x-2)^{r}=\sum_{r=0}^{2 n} b_{r}(x-3)^{r} \) and \( a_{k}=1 \) for all ....

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\( \sum_{r=0}^{2 n} a_{r}(x-2)^{r}=\sum_{r=0}^{2 n} b_{r}(x-3)^{r} \) and \( a_{k}=1 \) for all \( k \geq n \),
\( \mathrm{P} \)
then
(1) \( b_{n}={ }^{2 n} C_{n} \)
(2) \( b_{n}={ }^{2 n+1} C_{n-1} \)
(3) \( b_{n}={ }^{2 n+1} C_{n+1} \)
(4) None of these



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