X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200 求X等于多少?X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200求X等于多少?麻烦尽量分解详细点,不要只给答案,最好把规律找出来
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 15:35:36
![X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200 求X等于多少?X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200求X等于多少?麻烦尽量分解详细点,不要只给答案,最好把规律找出来](/uploads/image/z/4333601-65-1.jpg?t=X%2F%281%2B10%25%29%2BX%2F%281%2B10%25%292%2BX%2F%281%2B10%25%293%2BX%2F%281%2B10%25%294%2BX%2F%281%2B10%25%295%3D200+%E6%B1%82X%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3FX%2F%281%2B10%25%29%2BX%2F%281%2B10%25%292%2BX%2F%281%2B10%25%293%2BX%2F%281%2B10%25%294%2BX%2F%281%2B10%25%295%3D200%E6%B1%82X%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F%E9%BA%BB%E7%83%A6%E5%B0%BD%E9%87%8F%E5%88%86%E8%A7%A3%E8%AF%A6%E7%BB%86%E7%82%B9%2C%E4%B8%8D%E8%A6%81%E5%8F%AA%E7%BB%99%E7%AD%94%E6%A1%88%2C%E6%9C%80%E5%A5%BD%E6%8A%8A%E8%A7%84%E5%BE%8B%E6%89%BE%E5%87%BA%E6%9D%A5)
X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200 求X等于多少?X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200求X等于多少?麻烦尽量分解详细点,不要只给答案,最好把规律找出来
X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200 求X等于多少?
X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200
求X等于多少?
麻烦尽量分解详细点,不要只给答案,
最好把规律找出来
X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200 求X等于多少?X/(1+10%)+X/(1+10%)2+X/(1+10%)3+X/(1+10%)4+X/(1+10%)5=200求X等于多少?麻烦尽量分解详细点,不要只给答案,最好把规律找出来
分母的1、2、3、4是不是指数,是的话这是一个等比数列,公比q=1/1.1,用等比数列求和公式可以解出x.
推导一下公式,
上式简化为
xq+xq**2+xq**3+xq**4+xq**5=200
两边同乘q
xq**2+xq**3+xq**4+xq**5+xq**6=200q
后式减前式
200q-200=xq**6-xq
x=(200q-200)/(q**6-q)
把q=1/1.1代入
得x=(200/1.1-200)/(1/1.1**6-1/1.1)
太明显了吧亲~(1+10%)=1.1,提取公因式然后化为x/1.1(1+1/2+1/3+1/4+1/5)=200,就那么几个分数,算一下就行了,因为1+1/2+1/3+1/4+1/5……是没有公式的!答案是96.35
把每一项都提出一个1/(1+10%)来,剩下的是X+X/2+X/3+X/4+x/5=137/60X
合起来是1/(1+10%)*137/60X=200 得X=13200/137