一的三次方加二的三次方加三的三次方一直加到九的三次方等于多少

1^3+2^3+.+n^3=n^2(n+1)^2/4=[n(n+1)/2]^2 (n+1)^4-n^4=[(n+1)^2+n^2][(n+1)^2-n^2] =(2n^2+2n+1)(2n+1) =4n^3+6n^2+4n+1 2^4-1^4=4*1^3+6*1^2+4*1+1 3^4-2^4=4*2^3+6*2^2+4*2+1 4^4-3^4=4*3^3+6*3^2+4*3+1 . (n+1)^4-n^4=4*n^3+6*n^2+4*n+1 各式相加有