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

Evaluate : sum_(k=1)^n (2^k+3^(k-1))

sum _(k=1)^(n) tan^(-1). 1/(1+k+k^(2)) is equal to

""^(m)C_(r+1)+ sum_(k=m)^(n)""^(k)C_(r) is equal to :

sum_(k=0)^(5)(-1)^(k)2k

If k in R_o then det{adj(k I_n)} is equal to (A) K^(n-1) (B) K^((n-1)n) (C) K^n (D) k

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)

lim_(nrarroo) sum_(k=1)^(n)(k^(1//a{n^(a-(1)/(a))+k^(a-(1)/(a))}))/(n^(a+1)) is equal to

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

Find the value lim_(n rarr oo) sum_(k=2)^(n) cos^(-1) ((1 + sqrt((k -1) k(k + 1) (k + 2)))/(k(k + 1)))