Evaluate: `lim_(n->oo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]`

Evaluate lim_(n->oo)n[1/((n+1)(n+2))+1/((n+2)(n+4))+...+1/(6n^2)]

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

Evaluate: ("lim")_(n rarr oo)[(n !)/(n^n)]^(1//n)

Evaluate: ("lim")_(ntooo)(n^p sin^2 (n !))/(n+1)

Evaluate: lim_(n to infty) (n!)/((n+1)!-n!)

Evaluate: ("lim")_(nvecoo)((a1 1/x+a2 1/x++a n1/x)/n)^(n x)

Evaluate: ("lim")_(nvecoo)[1/(n^2)sec^2 1/(n^2)+2//n^2sec^2 4/(n^2)++1/nsec^2 1]

The value of (lim_(n->oo)[(2n)/(2n^2-1)cos(n+1)/(2n-1)-n/(1-2n)dot(n(-1)^n)/(n^2+1)]i s 1 (b) -1 (c) 0 (d) none of these

Evaluate lim_(ntooo) [(1+2+3+...+n)/(5n^2+2n+1)]

Find the value of sum_(n=1)^(infty) 1/(2n-1) (1/9^(n-1) + 1/9^(2n-1))