A) \[^{n+2}{{C}_{r}}\]
B) \[^{n+2}{{C}_{r+1}}\]
C) \[^{n+1}{{C}_{r}}\]
D) \[^{n+1}{{C}_{r+1}}\]
Correct Answer: B
Solution :
\[^{n}{{C}_{r+1}}{{+}^{n}}{{C}_{r}}{{=}^{n}}{{C}_{r+1}}\]. Now, \[^{n}{{C}_{r+1}}{{+}^{n}}{{C}_{r-1}}+{{2}^{n}}{{C}_{r}}\] \[{{=}^{n+1}}{{C}_{r+1}}{{+}^{n}}{{C}_{r}}{{+}^{n}}{{C}_{r-1}}{{+}^{n}}{{C}_{r}}\] \[{{=}^{n+1}}{{C}_{r+1}}{{+}^{n+1}}{{C}_{r}}\] \[{{=}^{n+2}}{{C}_{r+1}}\]You need to login to perform this action.
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