`Lim _(n rarr infty)(nsin(n!))/(n^2+1)= `

lim_(n rarr oo)(n+(-1)^(n))/(n)

Evaluate: lim_(n rarr infty)[1/n+1/(n+1)+1/(n+2)+ cdot cdot cdot +1/(3n)] .

lim_(n rarr0)n*sin(1/n)

(2) lim_(n rarr0) (n!sin x)/(n)

lim_(n rarr infty ) [((n+1)(n+2)...3n)/(n^(2n))]^(1//n) is equal to

The value of lim_(n rarr infty) (1)/(n) {(n+)(n+2)(n+3)…(n+n)}^(1//n) is equal to

lim_(n rarr infty) sum_(k=1)^(n) (n)/(n^(2)+k^(2)x^(2)),x gt 0 is equal to

Consider the following statements : I. lim_(n rarr infty) (2^(n)+(-2)^(n))/(2^(n)) does not exist II. lim_(n rarr infty)(3^(n)+(-3)^(n))/(4^(n)) does not exist Then

lim_(n rarr oo) (n(n+1))/(n^(2))= ________.

lim_(n rarr oo)(e^(2n)(n!)^(2))/(2n^(2n+1))