1*2+2*3+3*4……+19*20=多少，简便算法

来源：百度知道 编辑：UC知道 时间：2024/05/28 03:47:35

原式=1X（1+1）+2X（2+1）+3X（3+1）+...+19X（19+1）
=1X1+2X2+...+19X19+（1+2+...+19）
=19X（19+1）（19X2+1）/6 + 19X（1+19）/2
=190X13+190=190X14=2660

这类问题最好的方法是用递归
C语言完成:
#include <iostream.h>
const int NUMBER = 20;
int AddMul(int num)
{
if (num - 1 > 1)
{
return (num * (num -1)) + AddMul(num-1);
}
else
{
return (num * (num -1));
}
}
int main ()
{
int countallmul;
countallmul = AddMul(NUMBER);
cout << countallmul << endl;
return 0;
}
-------------------------------------------------------------
VB语言完成:
Private Sub Command1_Click()
Text1.Text = AddMul(20)
End Sub
Private Function AddMul(num As Integer) As Integer
If num - 1 > 1 Then
AddMul = AddMul(num - 1) + num * (num - 1)
Else
AddMul = num * (num - 1)
End If
End Function

(1*2+2*3)+(3*4+4*5)+(5*6+6*7)