`Lt_(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0`, is equal to (A) `k/e` (B) `e/k` (C) `1/(ke)` (D) none of these

Lt_(nrarroo) sum_(r=1)^n (2r)^k/n^(k+1),k!=-1 , is equal to (A) 2^k/(k-1) (B) 2^k/k (C) 1/(k+1) (D) 2^k/(k+1)

Lt_(nrarroo) sum_(r=1)^n (2r)^k/n^(k+1),k!=-1 , is equal to (A) 2^k/(k-1) (B) 2^k/k (C) 1/(k+1) (D) 2^k/(k+1)

lim_(n->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x (c) (log)_e x (d) none of these

Lt_(nrarroo)((n!)/n^n)^(1/n)= (A) e^(-2) (B) e^(-1) (C) e^3 (D) e

Lt_(nrarroo)((n!)/n^n)^(1/n)= (A) e^(-2) (B) e^(-1) (C) e^3 (D) e

lim_(n to oo) {(n!)/((kn)^n)}^(1/n) , where k != 0 is a constant and n in N , equals :

Let lim_(n rarr oo)(((kn)!)/(n^(kn)))^(1/n)=lambda(k) where k in N

lim_(nrarroo) sum_(r=1)^n 1/n e^(r/n) is (A) 1-e (B) e-1 (C) e (D) e+1

lim_(nrarroo) sum_(r=1)^n 1/n e^(r/n) is (A) 1-e (B) e-1 (C) e (D) e+1

" If "Lt_(nrarroo) ((prod_(k=1)^(n)(1+(k)/(n))))^(1/n)" has the value of equal to "ke^(-1)" where "k in N" ,then the value of "K" is "