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

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

" (e) "lim_(n rarr oo)[(n!)/(n^(n))]^(1/n)

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) (1+2^4+3^4+ … +n^4)/n^5-Lt_(nrarroo) (1+2^3+3^3 + … +n^3)/n^5 is (A) 1/5 (B) 1/30 (C) 0 (D) 1/4

lim_ (n rarr oo) [(e ^ ((1) / (n)) + e ^ ((2) / (n)) + e ^ ((3) / (n)) ++ e ^ ((n ) / (n))) / (n)]

lim_ (n rarr oo) {(e ^ (1 / n)) / (n ^ (2)) + (2 * (e ^ (1 / n)) ^ (2)) / (n ^ (2)) + (3 * (e ^ (1 / n)) ^ (3)) / (n ^ (2)) + ... + (n * (e ^ (1 / n)) ^ (n)) / ( n ^ (2))}

The value of lim_ (n rarr oo) [(1) / (n) + (e ^ ((1) / (n))) / (n) + (e ^ ((2) / (n))) / (n) + .... + (e ^ ((n-1) / (n))) / (n)] is:

int (e ^ (x) + (1) / (e ^ (n))) ^ (2)