Evaluate: `("lim")_(nvecoo)(n^psin^2(n !))/(n+1)`

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

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

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

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

Evaluate: ("lim")_(n->oo)(4^n+5^n)^(1/n)

Evaluate: ("lim")_(nvecoo)n^(-n^2){(n+2^0)(n+2^(-1))(n+2^(-2))(n+2^(-n+1))}^n

Evaluate: ("lim")_(nvecoo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(sqrt(3n^2)))

Evaluate: (lim)_(nvecoo)[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)] a. log(a/b) b. log(b/a) c. log(ab) d. None of these

Evaluate: ("lim")_(nvecoo)((1^2+2^2+3^3++n^2)(1^3+2^3+3^3++n^3))/(1^6+2^6+3^6++n^6)

Evaluate: ("lim")_(nvecoo)(sumr=1nsqrt(r)sumr=1n1/(sqrt(r)))/(sumr=1n r)