Question

一个小学奥数题怎么解?急

{（2*2*2-1）/（2*2*2+1）}*{（3*3*3-1）/（3*3*3*+1）}*{（4*4*4-1）/（4*4*4+1）}*...{（100*100*100-1）*（100*100*100+1）} =？？？

这个题目怎么解 过程是什么？还请高人指点 当然要用小孩子能懂的方法来回答。。因为是小学题。。

Answer 1

{（2*2*2-1）/（2*2*2+1）}*{（3*3*3-1）/（3*3*3*+1）}*{（4*4*4-1）/（4*4*4+1）}*...{（100*100*100-1）/（100*100*100+1）}
=[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)]
=[(2-1)(2^2+1^2+1*2)(3-1)(3^2+1^2+1*3)...(100-1)(100^2+1^2+1*100)]/[(2+1)(2^2+1^2-1*2)(3+1)(3^2+1^2-1*3)...(100+1)(100^2+1^2-1*100)]
=[1*2*(100^2+1^2+1*100)]/3*100*101=3367/5050
保证你对！

Answer 2

{（2*2*2-1）/（2*2*2+1）}*{（3*3*3-1）/（3*3*3*+1）}*{（4*4*4-1）/（4*4*4+1）}*...{（100*100*100-1）/（100*100*100+1）}
=[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)]
=[(2-1)(2^2+1^2+1*2)(3-1)(3^2+1^2+1*3)...(100-1)(100^2+1^2+1*100)]/[(2+1)(2^2+1^2-1*2)(3+1)(3^2+1^2-1*3)...(100+1)(100^2+1^2-1*100)]
=[1*2*(100^2+1^2+1*100)]/3*100*101=3367/5050
就可以了

Answer 3

我的妈呀！~~
{（2*2*2-1）/（2*2*2+1）}*{（3*3*3-1）/（3*3*3*+1）}*{（4*4*4-1）/（4*4*4+1）}*...{（100*100*100-1）/（100*100*100+1）}
=[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)]
=[(2-1)(2^2+1^2+1*2)(3-1)(3^2+1^2+1*3)...(100-1)(100^2+1^2+1*100)]/[(2+1)(2^2+1^2-1*2)(3+1)(3^2+1^2-1*3)...(100+1)(100^2+1^2-1*100)]
把各个括号里的数算出来最后消得
=[1*2*(100^2+1^2+1*100)]/3*100*101=3367/5050

Answer 4

现在要考好的初中，全要学奥数，国家又提倡不学奥数，做家长难，做小学生更难啊~~~~~~
{（2*2*2-1）/（2*2*2+1）}*{（3*3*3-1）/（3*3*3*+1）}*{（4*4*4-1）/（4*4*4+1）}*...{（100*100*100-1）/（100*100*100+1）}
=[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)]
=[(2-1)(2^2+1^2+1*2)(3-1)(3^2+1^2+1*3)...(100-1)(100^2+1^2+1*100)]/[(2+1)(2^2+1^2-1*2)(3+1)(3^2+1^2-1*3)...(100+1)(100^2+1^2-1*100)]
=[1*2*(100^2+1^2+1*100)]/3*100*101=3367/5050

Answer 5

{（2*2*2-1）/（2*2*2+1）}*{（3*3*3-1）/（3*3*3*+1）}*{（4*4*4-1）/（4*4*4+1）}*...{（100*100*100-1）/（100*100*100+1）}
=[(2^3-1)(3^3-1)...100^3-1)]/[(2^3+1)(3^3+1)...(100^3+1)]
=[(2-1)(2^2+1^2+1*2)(3-1)(3^2+1^2+1*3)...(100-1)(100^2+1^2+1*100)]/[(2+1)(2^2+1^2-1*2)(3+1)(3^2+1^2-1*3)...(100+1)(100^2+1^2-1*100)]
=[1*2*(100^2+1^2+1*100)]/3*100*101=3367/5050