k/(n^2+k^2)
= ( k / n^2 ) / { 1 + (k/n)^2 }
= (1/n) * ( k / n ) / { 1 + (k/n)^2 }

区分求積
lim[n→∞]納k=1,n]{k/(n^2+k^2)}
= ∫[0→1] { x / (1 + x^2 ) }