2n-2 is

lim_(n to oo) ((n)/(1 + n^2) + n/(2^2 + n^2) + n/(3^2 + n^2) + ……. + n/(n^2 + n^2)) is :

If =n(n^(2)-1^(2))(n^(2)-2^(2))(n^(2)-3^(2))......*(n^(2)-r^(2)),n>r,n in N then P is divisibe by (n^(2)-3^(2))......*(n^(2)-r^(2)),n>r,n in N

lim_(n to infty)((1)/(n^(2))+(2)/(n^(2))+(3)/(n^(2))+ . . . . +(n)/(n^(2))) is . . . . . . .

lim_(n to oo)((1)/(n^2)+(2)/(n^2)+(3)/(n^2)+"………."+(n)/(n^2)) is

lim_(n rarr oo) { n/(n^(2)+1^(2)) + n/(n^(2)+2^(2))+......+ n/(n^(2)+n^(2))} is equal to

lim_(n to oo ) {(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+ (n)/(n^(2)+n^(2))} is equal to

lim_(n to oo ) {(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+....+ (n)/(n^(2)+n^(2))} is equal to

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