lim n→∞ (√n+2√n+3√n+...+n√n)/(10n^5/2=lim n→∞ √n(1+2+3+...+n)/(10·(√n)^5=
=lim n→∞ √n[·n(n-1)/2]/(10·√n·(√n)^4)=lim n→∞ [(n(n-1)/2]/(10n²)=lim n→∞ (n-1)/20n=lim n→∞ (n/20n-1/20n)=lim n→∞(1/20-1/20n)=1/20 ( 1/20n → 0 dla n→∞ )
