There are "n" married couples at a path each person shakes hand with every person other than her or his spouse then number of handshakes is `f(n), (sum_(n=4)^(oo) 1/(f(n)))^(-1)`=?

Answer

6

Explanation

`f(n)=.^(2n)C_(2)-n=(2n(2n-1))/2-n`
`=n(2nn-1-1)=2n(n-1)`
`1/(f(n))=1/2.1/(n(n-1))=1/2 [1/(n-1)-1/n]`
`1/(f(4))=1/2[1/3-1/4]`
`impliessum_(n=4)^(oo) 1/(f(n))=1/2(1/3)=1/6`