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

lim_(n to oo) sum_(r=1)^(n) (1)/(n)e^(r//n) is

lim_(nrarroo) sum_(r=0)^(n-1) (1)/(sqrt(n^(2)-r^(2)))

lim_(nrarroo) (1-x+x.root n e)^(n) is equal to

The value of int_0^1lim_(n->oo)sum_(k =0)^n(x^(k+2)2^k)/(k!)dx is: (a) e ^(2) -1 (b) 2 (c) (e ^(2)-1)/(2) (d) (e ^(2) -1)/(4)

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

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

For x in R , lim_(xrarroo)((x-3)/(x+2))^x is equal to (a) e (b) e^(-1) (c) e^(-5) (d) e^5

If lim_(nrarroo)Sigma_(r=1)^(2n)(3r^(2))/(n^(3))e^((r^(3))/(n^(3)))=e^(a)-e^(b) , then a+b is equal to

Evaluate lim_(n->oo)1/nsum_(r=n+1)^(2n)log_e(1+r/n)

If a,b in R^(+) then find Lim_(nrarroo) sum_(k=1)^(n) ( n)/((k+an)(k+bn)) is equal to