1+3+5+7+...+(2n-5)+(2n-3)+(2n-1)+(2n+1)
问题描述:
1+3+5+7+...+(2n-5)+(2n-3)+(2n-1)+(2n+1)
答
1+3+5+7+...+(2n-5)+(2n-3)+(2n-1)+(2n+1)
=[1+(2n+1)]+[3+(2n-1)]+……+[(n-1)+(n+3)]+(n+1)
=(2n+2)+(2n+2)+……+(2n+2)+n+1
=(n/2)*(2n+2)+n+1
=n(n+1)+(n+1)
=(n+1)²
答
共有n+1项
根据等差公式
S=(2n+1+1)*(n+1)/2=(n+1)^2