1²+3²+5²+……+(2n-1)²=————

1²+3²+5²+……+(2n-1)²=————
1²+3²+5²+……+(2n-1)²=————

1²+3²+5²+……+(2n-1)²=————
(2n-1)^2=4n^2-4n+1
所以1^2+3^2+5^2+.+(2n-1)^2
=(4n^2+4(n-1)^2+.4*1^2)-4(n+(n-1)+.+1) +n
=4*1/6 n*(n+1)(2n+1) -4(n+1)n/2 +n
=2/3 n(n+1)(2n+1)-2(n+1)n +n
=2n(n+1)[(2n+1)/3-1]+n
=2n(n+1)(2n-1)/3 +n