Find `Lim {x->oo}{ (1+1/(n^2))^(2/n^2)(1+4/(n^2))^(4/n^2).....(1+(n^2)/(n^2))^(2n/n^2)}`

lim_(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

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

lim_(n to oo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+....+(1)/(n)]

lim_(n to oo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+....+(1)/(n)]

lim_(n->oo)(1/(n^2+1)+2/(n^2+2)+3/(n^2+3)+....n/(n^2+n))

lim_(n->oo)(1/(n^2+1)+2/(n^2+2)+3/(n^2+3)+....n/(n^2+n))

Lim {x rarr oo} {(1+ (1) / (n ^ (2))) ^ ((2) / (n ^ (2))) (1+ (4) / (n ^ (2)) ) ^ ((4) / (n ^ (2))) ...... (1+ (n ^ (2)) / (n ^ (2))) ^ (2 (n) / (n ^ (2)))}

If U_(n)=(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))^(2).............(1+(n^(2))/(n^(2)))^(n) m then lim_(n to oo)(U_(n))^((-4)/(n^(2))) is equal to

Evaluate : underset(n to oo) lim[((1+1^(2)/n^(2)))(1+(2^(2))/(n^(2)))(1+(3^(2))/(n^(2)))…(1+(n^(2))/(n^(2)))]^((1)/(n))