A) \[^{n+1}{{C}_{m+1}}\]
B) \[^{n-1}{{C}_{m-1}}\]
C) \[^{n}{{C}_{m}}\]
D) \[^{n}{{C}_{m+1}}\]
Correct Answer: A
Solution :
[a] \[^{m}{{C}_{m}}+{{\,}^{m+1}}{{C}_{m}}+.....+{{\,}^{n}}{{C}_{m}}\] \[{{=}^{m+1}}{{C}_{m+1}}+{{\,}^{m+1}}{{C}_{m}}+.....+{{\,}^{n}}{{C}_{m}}\] \[{{=}^{m+2}}{{C}_{m+1}}+{{\,}^{m+2}}{{C}_{m}}+.....+{{\,}^{n}}{{C}_{m}}\] \[={{\,}^{n}}{{C}_{m+1}}+{{\,}^{n}}{{C}_{m}}={{\,}^{n+1}}{{C}_{m+1}}\]
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