Given that
`lim_(nto oo) sum_(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1)/(2))`,
` lim_(n to oo) (1)/(n^k)[(n+1)^k(n+2)^k.....(n+n)^k]^(1//n)`, is

Given that lim_(n to oo)sum_(r=1)^(n)(log(n^(2)+r^(2))-2logn)/(n)=log2+(pi)/(2)-2 , then lim_(n to oo) (1)/(n^(2m))[(n^(2)+1^(2))^(m)(n^(2)+r^(2))^(m)......(n^(2))^(m)]^(1//n) is equal to

lim_(nto oo) (1)/(n^(2))sum_(r=1)^(n) re^(r//n)=

lim_(nto oo) (1)/(n^(2))sum_(r=1)^(n) re^(r//n)=

lim_(nto oo)sum_(r=1)^(n)r/(n^(2)+n+4) equals

lim_(nto oo)sum_(r=1)^(n)r/(n^(2)+n+4) equals

Evaluate lim_(n->oo)1/nsum_(r=n+1)^(2n)log_e(1+r/n)

lim_(n rarr oo) sum_(r=1)^(n) 1/n sec^(2) ((rpi)/(4n)) =

Find the value of lim_(n rarr oo)sum_(k=1)^(n)((k)/(n^(2)+k))