證明10ⁿ = 1000…0（n個0），其中n是任何非負整數

圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/mi/mi1.jpg


圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/mi/mi2.jpg


圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/mi/mi3.jpg


圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/mi/mi4.jpg


圖片參考：http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/mi/mi5.jpg


參考資料：
my pure maths knowledge

2009-07-09 21:03:14 補充：
http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/mi/mi1.jpg

2009-07-13 03:25:04 補充：
http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/mi/mi2.jpg
http://i476.photobucket.com/albums/rr124/paul2357paul/yahooknowledge/mi/mi3.jpg

全部都差少少野，留意題目係「非負整數」，
所以就算用MI，都應該係由「n=0」開始做。

由於10有1個0，每x10=加1個0

所以n次方就有n個0

除induction:

By definition, a^n = a * a *a * ... * a (from 1 to n) , in case of n>4
10^n is ,therefore, equals to 10 * 10 *10 *... * 10(from 1 to n)
By multiplication, we have 10^n = 10......0(n zeros),
which finishs the proof

但呢題題目係咪有玄機??咁淺易的做法doraemonpaul會問咩??

when n=1, 10^1=10

Assume it is true for n= k , where k belongs to positive integer ,

i.e. 10^k = 10...0

Consider n = k+1,

10^(k+1)=10^k x 10 = 10...0 x 10 = 10....00

it is true for n = k+1

By Mathematical induction , it is true for all positive integer n.

用mathematical induction是非常簡單的...