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7.Binomial Theorem
hard
$\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots .+\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$ ની કિમંત મેળવો.
A
$\frac{2^{50}}{50 !}$
B
$\frac{2^{50}}{51 !}$
C
$\frac{2^{51}}{51 !}$
D
$\frac{2^{51}}{50 \text { ! }}$
(JEE MAIN-2023)
Solution
$\sum \limits_{ r =1}^{26} \frac{1}{(2 r -1) !(51-(2 r -1)) !}=\sum \limits_{ r =1}^{26}{ }^{51} C _{(2 r -1)} \frac{1}{51 !}$
$=\frac{1}{51 !}\left\{{ }^{51} C _1+{ }^{51} C _3+\ldots .+{ }^{51} C _{51}\right\}$
$=\frac{1}{51 !}\left(2^{50}\right)$
Standard 11
Mathematics
