Find n if `(9^(3))^(2)=(3^(n))^(3)`

Find n if ""^(n-1)P_(3): ""^(n)P_(4) = 1:9 .

Find n if : a. ((4)/(49))^(5)xx((4)/(49))^(n-3)=((2)/(7))^(16) b. ((5)/(7))^(12)xx[((7)/(5))^(2)]^(8)=((7)/(5))^(2n-6) c. ((9)/(25))^(4)xx((9)/(25))^(n)=((3)/(5))^(12) d. ((3)/(5))^(20)xx[((5)/(3))^(3)]^(6)=((3)/(5))^(3n-13)

Find n if : 2P( n,3) = P(n+1,3)

Evaluate lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).

Find the sum of the n terms of the series whose nth term are given below : (i) 3n^(2)+2n (ii) 2n^(3)+4n+1 (iii) 2^(n)+3^(n) (iv) 3^(n)+n^(3)

Find n if : "" ^(2n)P_(n+1) : ""^(2n-2) P_n = 56 : 3

Find n if : P(2n, 3) = 100 P(n,2)

lim_(n to prop) (n)/(3){((3)/(n)+(9)/(n^(2)))^(2)+((3)/(n)+(18)/(n^(2)))^(2)+((3)/(n)+(27)/(n^(2)))^(2)+….+((3)/(n)+(9)/(n))^(2)} is less than or equal to

If (9^n*3^2*(3^(-n/2))^(-2)-(27)^n)/(3^(3m)*2^3)=1/(27), Prove that m-n=1.