જો `((2n)!)/(3!(2n-3)!)અને(n!)/(2!(n-2)!)` ગુણોત્તર `44 :3માં હોય, તો `ndot` શોધો

If ((2n)!)/(3!(2n-3)!) and (n!)/(2!(n-2)!) are in the ratio 44:3 find 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 ((2n!))/((3!)xx(2n-3)!): (n!)/((2!)xx(n-2)!)=44:3 , find the value of n.

Prove that ((2n)!)/(2^(2n)(n!)^(2))<=(1)/(sqrt(3n+1)) for all n in N

lim_(n rarr oo)(2^(3n))/(3^(2n))=

lim_(n rarr oo)(3^(n+1)+2^(n+2))/(3^(n-1)+2^(n-2)) =

(3xx9^(n+1)-9xx3^(2n))/(3xx3^(2n+3)-9^(n+1))

If ^(2n)C_(3):^(n)C_(2)=44:3,f in dn

(1^(3)+2^(3)+...+n^(3))/(1+3+5+...+(2n-1))=((n+1)^( 2))/(4)