Question

）“数学王子”高斯从小就善于观察和思考．在他读小学时就能在课堂上快速地计算出1+2+3+…+98+99+100=505

Answer 1

1+2+3...+n① n个数,求和 n(n+1)/2

2+3+4...n+1② 也是n个数,求和 n(2+n+1)/2

①+②=168

(n(n+1)+n(n+3))/2 =n(n+2)=168

n=12

3+5+7+…+（2n+1）有n项

3+5+7+…+（2n+1）= n(3+2n+1)/2=n(n+2)=168

n=12