Question

如何推导“1方+2方+3方+……+n方=1/6n(n+1)(2n+1)”

Answer 1

1^2=1/6*1（2*1+1）（1+1）=1/6*6=11^2+2^2=1/6*（2*2+1）（2+1）=1/6*30=5.假设1方+2方+3方+……+N方=1/6n（2n+1)(n+1)则1^2+2^2+3^2+……+n^2+（n+1）^2=1/6n（2n+1)(n+1)+(n+1)^2=1/6(n+1)(2n^2+n+6n+6)=1/6*(n+1...