Lt[(1)/(1-n^(2))+(2)/(1-n^(2))+....+(n)/(1-n^(2))]=

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

Lt_(ntooo)[(1)/(1-n^(2))+(2)/(1-n^(2))+.......+(n)/(1-n^(2))]=

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

Lt_(ntooo)[(1)/(1+n^(2))+(2)/(1+n^(2))+.............+(n)/(1+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]=

Lt_(n rarr oo)[(1+(1)/(n^(2)))^((2)/(n^(2)))(1+(2^(2))/(n^(2)))^((4)/(n^(2)))(1+(3^(2))/(n^(2)))^((6)/(n^(2))).....(1+(n^(2))/(n^(2)))^((2n)/(n^(2)))]