Question

1²+2²+3²+...+n²的公式,

Answer 1

这个是平方和公式.

设个未知数Y吧

Y=1²+2²+3²+n²

Y=1x1+2x2+3x3+n²

∴y=1x(2-1)+2x(3-1）+3x(4-1)……+nx(n+1-1)

=1x2+2x3+3x4……n(n+1)-n(n+1)/2

又∵n(n+1)=1/3(n(n+1)(n+2)-n(n-1)(n+1))

∴y=1/3(1x2x3-0x1x2)……1/3(nx(n+1)(n+2)-n(n-1)(n+1))-n(n+1)/2

所以Y=n(n+1)(2n+1)/6