求数列1^k+2^k+3^k+...+n^k的和如题,已求出当k=1时值为1/2n^2+1/2n,当k=2时值为1/3n^3+1/2n^2+1/6n,当k=3时值为1/4n^4+1/2n^3+1/4n^2,当k=4时值为1/5n^5+1/2n^4+1/3n^3-1/30n求1^k+2^k+3^k+...+n^k的和请告诉我怎么从上面的东

Question

求数列1^k+2^k+3^k+...+n^k的和
如题,已求出当k=1时值为1/2n^2+1/2n,当k=2时值为1/3n^3+1/2n^2+1/6n,当k=3时值为1/4n^4+1/2n^3+1/4n^2,当k=4时值为1/5n^5+1/2n^4+1/3n^3-1/30n
求1^k+2^k+3^k+...+n^k的和
请告诉我怎么从上面的东西求得

Answer 1

讲一下推倒过程吧,k=1时是等差数列,都会.k=2时,（n-1)^3=n^3-3n^2+3n-1(n-2)^3=(n-1)^3-3(n-1)^2+3(n-1)-1...1^3=2^3-3*2^2+3*2-1累加,得1=n^3-3(2^2+.n^2)+3(2+3+...n)-(n-1)到了这一步,想必结果就已经出来了.所以...