作业帮一道数学题,就说有技巧的是这样的:[1/2 / (1+1/2)] + [1/3 /(1+1/2)(1+1/3)]`````````````` [1/1999 / (1+1/2)(1+1/3)```````(1+1/1999)]=?怎么算啊,
来源：学生作业帮助网 编辑：作业帮 时间：2024/10/08 14:56:29
![一道数学题,就说有技巧的是这样的:[1/2 / (1+1/2)] + [1/3 /(1+1/2)(1+1/3)]`````````````` [1/1999 / (1+1/2)(1+1/3)```````(1+1/1999)]=?怎么算啊,](/uploads/image/z/5541414-6-4.jpg?t=%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E5%B0%B1%E8%AF%B4%E6%9C%89%E6%8A%80%E5%B7%A7%E7%9A%84%E6%98%AF%E8%BF%99%E6%A0%B7%E7%9A%84%3A%5B1%2F2+%2F+%281%2B1%2F2%29%5D+%2B+%5B1%2F3+%2F%281%2B1%2F2%29%281%2B1%2F3%29%5D%60%60%60%60%60%60%60%60%60%60%60%60%60%60+%5B1%2F1999+%2F+%281%2B1%2F2%29%281%2B1%2F3%29%60%60%60%60%60%60%60%281%2B1%2F1999%29%5D%3D%3F%E6%80%8E%E4%B9%88%E7%AE%97%E5%95%8A%2C)
一道数学题,就说有技巧的是这样的:[1/2 / (1+1/2)] + [1/3 /(1+1/2)(1+1/3)]`````````````` [1/1999 / (1+1/2)(1+1/3)```````(1+1/1999)]=?怎么算啊,
一道数学题,就说有技巧的
是这样的:[1/2 / (1+1/2)] + [1/3 /(1+1/2)(1+1/3)]`````````````` [1/1999 / (1+1/2)(1+1/3)```````(1+1/1999)]=?
怎么算啊,
一道数学题,就说有技巧的是这样的:[1/2 / (1+1/2)] + [1/3 /(1+1/2)(1+1/3)]`````````````` [1/1999 / (1+1/2)(1+1/3)```````(1+1/1999)]=?怎么算啊,
首先,把作为变量的分母设为N,不难发现1/N除以1+1/N=1/N+1然后可以发现第一个中夸好里的商等于1/N+1(此时N=2).第二个则等于1/N+3,再接下来等于己于1/(N+6),1/(N+10),1/(N+15),可以把N+.设为T,则分母N+1,N+3,N+6,N+10.依小到大分别为分母,T=1
3,6,10,15,21,28,37,.T的大小变化为T1+2=T2,T2+3=T3 T3+4=T5所以,T的变化规律是+2...+3...+4...+5...只要知道分母N,（已知）再知道T的变化规律就可以了(如上述).我们还可以发现,1/N除以(.乘以N+1/N)始终等于1/N乘以2/N+1.最后,只要把1/N+T1+1/N+T2+1/N+T3.为了计算简便,我们可以把T提出来再加上1/N1+1/N2+.N(已知),T的变化规律如上述.方法是这样的,计算嘛,就劳您大驾了.