`lim_(n rarroo) [1+2/n]^(2n)=`

Evaluate the following define integrals as limit of sums : lim_(n rarroo) [(1+1/n) (1+2/n)......(1+n/n)]^(1//n)

lim_(n rarr oo) [1/(2n+1)+1/(2n+2)+…….+1/(2n+n)]=

lim_(n rarr oo) ((1)/(1-n^(2)) + (2)/(1-n^(2)) +…...+(n)/(1-n^(2))) is :

lim (n rarroo) [(1)/(n)+(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+...+(n)/(n^(2)+(n-1)^(2))]

lim_ (n rarr oo) [(1) / (1-n ^ (2)) + (2) / (1-n ^ (2)) + ... + (n) / (1-n ^ (2 ))] is

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