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

Evaluate lim_(nto oo)((n+2)!+(n+1)!)/((n+2)!-(n+1)!)

Evaluate: lim_(n rarr oo)[(1)/((n+1)^(2))+(1)/((n+2)^(2))+...+(1)/((2n)^(2))]

Evalute lim_ (n rarr oo) [(1) / ((n + 1) (n + 2)) + (1) / ((n + 2) (n + 4)) + ...... + ( 1) / (6n ^ (2))]

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

Evaluate :lim_(n rarr oo)sum_(r=1)^(n)(1)/((n^(2)+r^(2))^(1/2))

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

Evaluate lim_ (n rarr oo) [(1+ (1) / (n)) 91+ (2) / (n)) .... (1+ (n) / (n))] ^ ((1) /(a))

Evaluate: lim_(n rarr oo)[(1)/(n^(2))sec^(2)(1)/(n^(2))+2/n^(2)sec^(2)(4)/(n^(2))+...+(1)/(n)sec^(2)1]]