A) \[{{2}^{19}}-\frac{\left( ^{20}{{C}_{10}}+{{\,}^{20}}{{C}_{9}} \right)}{2}\]
B) \[{{2}^{19}}-\frac{\left( ^{20}{{C}_{10}}+\,2{{\times }^{20}}{{C}_{9}} \right)}{2}\]
C) \[{{2}^{19}}-\frac{^{20}{{C}_{10}}}{2}\]
D) None of these
Correct Answer: B
Solution :
[b] Given series is \[^{20}{{C}_{0}}+{{\,}^{20}}{{C}_{1}}+{{\,}^{20}}{{C}_{2}}+...+{{\,}^{28}}{{C}_{8}}\] \[=\frac{({{2}^{20}}-{{\,}^{20}}{{C}_{10}})}{2}-{{\,}^{20}}{{C}_{9}}\] \[={{2}^{19}}-\frac{({{\,}^{20}}{{C}_{10}}+2\times {{\,}^{20}}{{C}_{9}})}{2}\]You need to login to perform this action.
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