Find the values of `(1)/(12!) + (1)/(10! 2!) + (1)/(8!4!) + …+ (1)/(12!)`

Explanation

` because 0 ! = 1`
` therefore ` The given series can be writtten as
`(1)/(12!0!)+ (1)/(10!2!) + (1)/(8!4 !) + ... + (1)/(0!12!)` ...(i)
`because ` Sum pf values of eacj terms in factorial are equal
i.e., ` 12 + 0 = 10 + 2 = 8 + 4 = ...= 12 `
From Eq . (i) `(1)/(12!)[(1)/(12!0!)+ (1)/(10!2!) + (1)/(8!4 !) + ... + (1)/(0!12!)]`
`(1)/(12!) (""^(12)C_(0) +""^(12)C_(2) + ""^(12)C_(4) + ...+ ""^(12)C_(12)) = (2^(12-1))/(12!) = (2^(11))/(12!)` .