本帖最後由 『玩』” 於 19-6-2009 00:12 編輯
41# 『玩』”
Given that jojo win10次影 before
let p(n) be the statement ''jojo win n次 影=right" ,n= win的場數
when n =1
jojo win1次 影
Assume p(j) is true
such that jojo win j 次 ...
jaxis 發表於 18-6-2009 23:14 
in conclusion:
you would like to prove ''jojo is differ from 影"?
今次認真prove!
Given that jojo win10次影 before,
let p(n) be the proposition that ''jojo win 1次 影+ jojo win 2次 影+ ... + jojo win n次 影 = [(n+1)n]/2 right" ,where n = win的場數 which is a positive integer.
when n =1
LFS:
jojo win1次 影
RHS:
=2(1)/2 right
=(1)right
since jojo win10次影 before(given)
jojo win1次 影 = right
so p(1) is true
Assume p(k) is true for any positive integer k,
i.e. jojo win 1次 影+ jojo win 2次 影+ ... + jojo win k 次 影 = [(k+1)k]/2 right , where k=win的場數 which is a positive integer
when n=k+1
jojo win 1次 影+ jojo win 2次 影+ ... + jojo win k次 影+jojo win k+1次 影 = [(k+1)k]/2 right + jojo win k+1次 影
=[(k+1)k]/2 right + jojo win 1次 影+jojo win k次 影
=[(k+1)k]/2 right + right + k right (since jojo win10次影 before(given) & jojo win1次 影=right)
=[(k+1)k]/2 right + (1+k)right
=1/2(k+1)(k right + 2 right)
=1/2(k+1)(k+2) right
=1/2(k+1)[(k+1)+1]right
so p(k+1) is also true
By the principle of mathematical induction ,p(n) is true for all positive integer n . |