If `(n!)/(2.(n-2)!):(n!)/(4!.(n-4)!)=2:1`, find the value of n

(i) If (n!)/(2.(n-2)!): (n!)/(4!.(n-4)!) = 2:1 , find the valye of n. (ii) If ((2n)!)/(3!(2n-3)!): (n!)/(2!(n-2)!) = 44:3 , then find the value of n.

If (n !)/(2!(n-2)!) and (n !)/(4!(n-4)!) are in the ratio 2:1 , find the value of ndot

If (n!)/( 2!( n-2) !) and (eta !)/( 4!(n-4)!) are in the ratio 2: 1 , find the value of n.

If .^(n)P_(4): .^(n)P_(5) = 1:2 , find the value of n.

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of n .

If f(n)=|(n!, (n+1)!, (n+2)!),((n+1)!, (n+2)!, (n+3)!), ((n+2)!, (n+3)!, (n+4)!)| Then the value of 1/1020[(f(100))/(f(99))] is

If m,n in N and m=(n^2-n-35)/(n-4) , then find the value of m.

If P(n ,4)=20xxP(n ,2), then find the value of n

If sum_(n=0)^oo2cot^(-1) ((n^2+n-4)/2)=kpi then find the value of k

Let S_(n)=""^(n)C_(0)""^(n)C_(1)+""^(n)C_(1)""^(n)C_(2)+…..+""^(n)C_(n-1)""^(n)C_(n). "If" (S_(n+1))/(S_(n))=(15)/(4) , find the sum of all possible values of n (n in N)