设A=1+3+5+7…+（2n+1）①,
所以A=（2n+1）+(2n-1)+(2n-3)+……+1②
①+②=[1+(2n+1)]+[3+(2n-1)]+……+[(2n+1)+1]
=(2n+2)+(2n+2)+……(2n+2) {共N+1项}
=(n+1)*(2n+2)
=2(n+1)^2=2A
所以A=（n+1）^2
(注：^2是平方的意思)