證明10ⁿ = 1000…0（n個0），其中n是任何非負整數
回答 (7)
2009-07-10 5:02 am
✔ 最佳答案
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
2009-07-04 2:39 pm
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。
所以就算用MI，都應該係由「n=0」開始做。
2009-06-30 6:29 am
由於10有1個0，每x10=加1個0
所以n次方就有n個0
所以n次方就有n個0
2009-06-29 8:27 am
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
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
2009-06-29 5:46 am
但呢題題目係咪有玄機??咁淺易的做法doraemonpaul會問咩??
2009-06-29 1:24 am
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.
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.
2009-06-29 12:48 am
用mathematical induction是非常簡單的...
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