" 04."Lt_(n rarr oo)(1)/(1+n^(2))+(2)/(2+n^(2))+...+(n)/(n+n^(2))

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

{:(" "Lt),(n rarr oo):} [(1)/(1-n^(2))+(2)/(1-n^(2))+...+(n)/(1-n^(2))]=

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

Evaluate :(lim_(x rarr oo))_(x rarr oo)(1)/(1+n^(2))+(1)/(2+n^(2))+...+(n)/(n+n^(2))

Lt_(x to oo)[(1)/(n^(2)-1)+(2)/(n^(2)-1)+....+(n)/(n^(2)-1)]=

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

{:(" "Lt),(n rarr oo):} [ (1)/(n^(2)) sec^(2). (1)/(n^(2)) + (2)/(n^(2))sec^(2). (4)/(n^(2))+...+1/n sec^(2)1]=

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