納k=1,n]{k^4-(k-1)^4}=納k=1,n]{4k^3-6k^2+4k-1}
n^4=4納k=1,n](k^3)-n(n+1)(2n+1)+2n(n+1)-n
n^4+n(n+1)(2n+1)-2n(n+1)+n=4納k=1,n](k^3)
n(n+1)(n^2-n+1)+n(n+1)(2n+1)-2n(n+1)=4納k=1,n](k^3)
n(n+1)(n^2-n+1+2n+1-2)=4納k=1,n](k^3)
n^2(n+1)^2=4納k=1,n](k^3)