A) \[^{n+1}{{C}_{r}}\]
B) \[^{n+1}{{C}_{r+1}}\]
C) \[^{n+2}{{C}_{r}}\]
D) \[{{2}^{n}}\]
Correct Answer: B
Solution :
\[^{r}{{C}_{r}}{{+}^{r+1}}{{C}_{r}}{{+}^{r+2}}{{C}_{r}}......{{+}^{n-1}}{{C}_{r}}{{+}^{n}}{{C}_{r}}\] \[{{=}^{r+1}}{{C}_{r+1}}{{+}^{r+1}}{{C}_{r}}{{+}^{r+2}}{{C}_{r}}+.....{{+}^{n-1}}{{C}_{r}}{{+}^{n}}{{C}_{r}}\] \[{{=}^{r+2}}{{C}_{r+1}}{{+}^{r+2}}{{C}_{r}}+.....{{+}^{n-1}}{{C}_{r}}{{+}^{n}}{{C}_{r}}\] \[{{=}^{r+3}}{{C}_{r+1}}+......{{+}^{n-1}}{{C}_{r}}{{+}^{n}}{{C}_{r}}\]. On solving similar way, we get \[^{n-1}{{C}_{r+1}}{{+}^{n}}{{C}_{r}}{{+}^{n}}{{C}_{r}}{{=}^{n}}{{C}_{r+1}}{{+}^{n}}{{C}_{r}}{{=}^{n+1}}{{C}_{r+1}}\].You need to login to perform this action.
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