A) \[{{2}^{40}}+\frac{40!}{{{(20!)}^{2}}}\]
B) \[{{2}^{39}}-\frac{1}{2}\times \frac{40!}{{{(20!)}^{2}}}\]
C) \[{{2}^{39}}{{+}^{40}}{{C}_{20}}\]
D) None of these
Correct Answer: D
Solution :
\[^{40}{{C}_{0}}{{+}^{40}}{{C}_{1}}{{+}^{40}}{{C}_{2}}+...{{+}^{40}}{{C}_{20}}\] \[=\frac{1}{2}[{{2.}^{40}}{{C}_{0}}+{{2.}^{40}}{{C}_{1}}+{{2.}^{40}}{{C}_{2}}+...+{{2.}^{40}}{{C}_{20}}]\] \[=\frac{1}{2}[{{(}^{40}}{{C}_{0}}{{+}^{40}}{{C}_{40}})+{{(}^{40}}{{C}_{1}}{{+}^{40}}{{C}_{39}})+...+\] \[{{(}^{40}}{{C}_{19}}{{+}^{40}}{{C}_{21}})+{{2}^{40}}{{C}_{20}}]\] \[=\frac{1}{2}[{{\{}^{40}}{{C}_{0}}{{+}^{40}}{{C}_{1}}{{+}^{40}}{{C}_{2}}+...{{+}^{40}}{{C}_{19}}{{+}^{40}}{{C}_{20}}]\] \[{{+}^{40}}{{C}_{21}}\}{{+}^{40}}{{C}_{20}}]\] \[=\frac{1}{2}\left[ {{2}^{40}}+\frac{40!}{{{(20!)}^{2}}} \right]={{2}^{39}}+\frac{1}{2}\frac{40!}{{{(20!)}^{2}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
