If `lim(n->oo)(n*3^n)/(n(x-2)^n +n*3^(n+1)-3^n) = 1/3` then the range of x is (where `n epsilon N`)

lim_(n->oo)((n^2-n+1)/(n^2-n-1))^(n(n-1)) is

If n! +(n-1) ! =3, then find the value of n.

Evaluate: lim_(n->oo)(((n+1)(n+2)...(n+n))^(1/n))/n

If .^(n+5) P_(n +1) = ((11(n-1))/2) .^(n +3) P_(n) then the value of n are

In .^(2n)C_(3) :.^(n)C_(3) = 11 : 1 then n is

If L=("lim")_(nvecoo)(2x3^2x2^3x3^4..... x2^(n-1)x3^n)^(1/((n^(2+1))) , then the value of L^4 is

lim_(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n) is equal to

lim_(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) 2 (c) 4 (d) oo

The value of lim_(x->oo)((2^(x^n))^(1/e^x)-(3^(x^n))^(1/e^x))/(x^n) (where n in N) is (a) logn(2/3) (b) 0 (c) nlogn(2/3) (d) none of defined