1+3=4=2² 1+3+5==9=3² 试猜想1+3+5+7+9+…+(2n-1)+(2n+1)+(2n+3)=
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![1+3=4=2² 1+3+5==9=3² 试猜想1+3+5+7+9+…+(2n-1)+(2n+1)+(2n+3)=](/uploads/image/z/388801-1-1.jpg?t=1%2B3%3D4%3D2%26%23178%3B+1%2B3%2B5%3D%3D9%3D3%26%23178%3B+%E8%AF%95%E7%8C%9C%E6%83%B31%2B3%2B5%2B7%2B9%2B%E2%80%A6%2B%EF%BC%882n-1%EF%BC%89%2B%EF%BC%882n%2B1%EF%BC%89%2B%EF%BC%882n%2B3%29%3D)
1+3=4=2² 1+3+5==9=3² 试猜想1+3+5+7+9+…+(2n-1)+(2n+1)+(2n+3)=
1+3=4=2² 1+3+5==9=3² 试猜想1+3+5+7+9+…+(2n-1)+(2n+1)+(2n+3)=
1+3=4=2² 1+3+5==9=3² 试猜想1+3+5+7+9+…+(2n-1)+(2n+1)+(2n+3)=
可推知规律为和=[(1+末项)/2]².
所以1+3+5+7+9+…+(2n-1)+(2n+1)+(2n+3)=[(1+2n+3)/2]²=(n+2)².